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- La ecuación:
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Ecuación 12/(x+3)=-6/7
-
Ecuación (x-6)(4x-6)=0
-
Ecuación (x+7)^3=9*(x+7)
-
Ecuación z^2+z+1=0
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 7*x-1*y=0
- -9*x-1*y=6
- -2*x+2*y=4
-
Expresiones idénticas
- log(y^ tres + cinco)/ tres =(c-log(x^ tres + cinco))/ tres
- logaritmo de (y al cubo más 5) dividir por 3 es igual a (c menos logaritmo de (x al cubo más 5)) dividir por 3
- logaritmo de (y en el grado tres más cinco) dividir por tres es igual a (c menos logaritmo de (x en el grado tres más cinco)) dividir por tres
- log(y3+5)/3=(c-log(x3+5))/3
- logy3+5/3=c-logx3+5/3
- log(y³+5)/3=(c-log(x³+5))/3
- log(y en el grado 3+5)/3=(c-log(x en el grado 3+5))/3
- logy^3+5/3=c-logx^3+5/3
- log(y^3+5) dividir por 3=(c-log(x^3+5)) dividir por 3
-
Expresiones semejantes
- log(y^3+5)/3=(c+log(x^3+5))/3
- log(y^3-5)/3=(c-log(x^3+5))/3
- log(y^3+5)/3=(c-log(x^3-5))/3
-
Expresiones con funciones
- Logaritmo log
- log(3)*27=x
- log(1)/9=2+x
- log(4/(7-x))/log(x^2)=11
- log(y+1)=Const-log(x-1)
- log(4*3^(x-1)-1)/log(3)=2*x-1
- Logaritmo log
- log(3)*27=x
- log(1)/9=2+x
- log(4/(7-x))/log(x^2)=11
- log(y+1)=Const-log(x-1)
- log(4*3^(x-1)-1)/log(3)=2*x-1
log(y^3+5)/3=(c-log(x^3+5))/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 3 \ / 3 \
log\y + 5/ c - log\x + 5/
----------- = ---------------
3 3
$$\frac{\log{\left(y^{3} + 5 \right)}}{3} = \frac{c - \log{\left(x^{3} + 5 \right)}}{3}$$
Gráfica
Respuesta rápida
[src]
/ / / / c \ / c \\\ / / / c \ / c \\\\ / / / c \ / c \\\ / / / c \ / c \\\
| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||
| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||
| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||
| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|
| / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / |-5 + re|------|| + im |------| *cos|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *sin|----------------------------------|
| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /
| \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y /
x1 = I*|- --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------
\ 2 2 / 2 2
$$x_{1} = i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}$$
/ / / / c \ / c \\\ / / / c \ / c \\\\ / / / c \ / c \\\ / / / c \ / c \\\
| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||
| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||
| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||
| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|
| / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / |-5 + re|------|| + im |------| *cos|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *sin|----------------------------------|
| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /
| \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y /
x2 = I*|- --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------
\ 2 2 / 2 2
$$x_{2} = i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}$$
/ / / c \ / c \\\ / / / c \ / c \\\
__________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||
/ 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||
/ / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||
/ | | e || 2| e | | \ \5 + y / \5 + y //| / | | e || 2| e | | \ \5 + y / \5 + y //|
x3 = / |-5 + re|------|| + im |------| *cos|----------------------------------| + I* / |-5 + re|------|| + im |------| *sin|----------------------------------|
6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /
\/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y /
$$x_{3} = i \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)} + \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}$$
x3 = i*((re(exp(c)/(y^3 + 5)) - 5)^2 + im(exp(c)/(y^3 + 5))^2)^(1/6)*sin(atan2(im(exp(c)/(y^3 + 5), re(exp(c)/(y^3 + 5)) - 5)/3) + ((re(exp(c)/(y^3 + 5)) - 5)^2 + im(exp(c)/(y^3 + 5))^2)^(1/6)*cos(atan2(im(exp(c)/(y^3 + 5)), re(exp(c)/(y^3 + 5)) - 5)/3))
Suma y producto de raíces
[src]
suma
/ / / / c \ / c \\\ / / / c \ / c \\\\ / / / c \ / c \\\ / / / c \ / c \\\ / / / / c \ / c \\\ / / / c \ / c \\\\ / / / c \ / c \\\ / / / c \ / c \\\
| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e ||| | __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||
| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------||| | / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||
| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3||| | / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3||| / / / c \ / c \\\ / / / c \ / c \\\
| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //| | / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||
| / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / |-5 + re|------|| + im |------| *cos|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *sin|----------------------------------| | / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / |-5 + re|------|| + im |------| *cos|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *sin|----------------------------------| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||
| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 / | 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 / / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||
| \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / / | | e || 2| e | | \ \5 + y / \5 + y //| / | | e || 2| e | | \ \5 + y / \5 + y //|
I*|- --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- + I*|- --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + / |-5 + re|------|| + im |------| *cos|----------------------------------| + I* / |-5 + re|------|| + im |------| *sin|----------------------------------|
\ 2 2 / 2 2 \ 2 2 / 2 2 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /
\/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y /
$$\left(i \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)} + \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}\right) + \left(\left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) + \left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right)\right)$$
=
/ / / / c \ / c \\\ / / / c \ / c \\\\ / / / / c \ / c \\\ / / / c \ / c \\\\
| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| | __________________________________ | | | e | | e ||| __________________________________ | | | e | | e ||||
| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| | / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------||||
| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| | / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \ / c \\\
| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| | / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| __________________________________ | | | e | | e |||
| / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| | / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / 2 |atan2|im|------|, -5 + re|------|||
| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| | 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| / / / c \\ / c \ | | | 3| | 3|||
| \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | / | | e || 2| e | | \ \5 + y / \5 + y //|
I*|- --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------| + I*|- --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------| + I* / |-5 + re|------|| + im |------| *sin|----------------------------------|
\ 2 2 / \ 2 2 / 6 / | | 3|| | 3| \ 3 /
\/ \ \5 + y // \5 + y /
$$i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) + i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) + i \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}$$
producto
/ / / / / c \ / c \\\ / / / c \ / c \\\\ / / / c \ / c \\\ / / / c \ / c \\\\ / / / / / c \ / c \\\ / / / c \ / c \\\\ / / / c \ / c \\\ / / / c \ / c \\\\
| | __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| | | __________________________________ | | | e | | e ||| __________________________________ | | | e | | e |||| __________________________________ | | | e | | e ||| __________________________________ | | | e | | e ||||
| | / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| | | / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------|||| / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------||||
| | / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| | | / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3|||| / / / / c \ / c \\\ / / / c \ / c \\\\
| | / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| | | / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| / | | e || 2| e | | \ \5 + y / \5 + y //| ___ / | | e || 2| e | | \ \5 + y / \5 + y //|| | __________________________________ | | | e | | e ||| __________________________________ | | | e | | e ||||
| | / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / |-5 + re|------|| + im |------| *cos|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *sin|----------------------------------|| | | / |-5 + re|------|| + im |------| *sin|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *cos|----------------------------------|| / |-5 + re|------|| + im |------| *cos|----------------------------------| \/ 3 * / |-5 + re|------|| + im |------| *sin|----------------------------------|| | / 2 |atan2|im|------|, -5 + re|------||| / 2 |atan2|im|------|, -5 + re|------||||
| | 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| | | 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| 6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /| | / / / c \\ / c \ | | | 3| | 3||| / / / c \\ / c \ | | | 3| | 3||||
| | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | | | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / | | / | | e || 2| e | | \ \5 + y / \5 + y //| / | | e || 2| e | | \ \5 + y / \5 + y //||
|I*|- --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------|*|I*|- --------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------| - --------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------|*| / |-5 + re|------|| + im |------| *cos|----------------------------------| + I* / |-5 + re|------|| + im |------| *sin|----------------------------------||
\ \ 2 2 / 2 2 / \ \ 2 2 / 2 2 / |6 / | | 3|| | 3| \ 3 / 6 / | | 3|| | 3| \ 3 /|
\\/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / /
$$\left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) \left(i \left(- \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{2}\right) \left(i \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)} + \sqrt[6]{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}\right)$$
=
/ / / c \ / / / c \ / c \\\\ \
| | | e | | | | e | | e |||| |
| | im|------| |atan2|im|------|, -5 + re|------|||| |
| | | 3| | | | 3| | 3|||| |
| | \5 + y / | \ \5 + y / \5 + y //|| |
| 3*I*|----------------------------------------- + sin|----------------------------------|| |
| / / / c \ / c \\\ | __________________________________ \ 3 /| |
| | | | e | | e ||| | / 2 | |
| / / / c \ / c \\\ |atan2|im|------|, -5 + re|------||| / / / c \ / c \\\ | / / / c \\ / c \ | / c \ |
| | | | e | | e ||| | | | 3| | 3||| | | | e | | e ||| | / | | e || 2| e | | | e | |
________________________________________________ | |atan2|im|------|, -5 + re|------||| | \ \5 + y / \5 + y //| |atan2|im|------|, -5 + re|------||| | / |-5 + re|------|| + im |------| | 3*re|------| |
/ / c \ / c \ / c \ | | | | 3| | 3||| 3*cos|----------------------------------| | | | 3| | 3||| | / | | 3|| | 3| | | 3| |
/ 2| e | 2| e | | e | | 3| \ \5 + y / \5 + y //| 15 \ 3 / 3| \ \5 + y / \5 + y //| \\/ \ \5 + y // \5 + y / / \5 + y / |
/ 25 + im |------| + re |------| - 10*re|------| *|cos |----------------------------------| - ------------------------------------------- - ----------------------------------------- - I*sin |----------------------------------| + ----------------------------------------------------------------------------------------- + -------------------------------------------|
/ | 3| | 3| | 3| | \ 3 / __________________________________ 4 \ 3 / 4 __________________________________|
\/ \5 + y / \5 + y / \5 + y / | / 2 / 2 |
| / / / c \\ / c \ / / / c \\ / c \ |
| / | | e || 2| e | / | | e || 2| e | |
| 4* / |-5 + re|------|| + im |------| 4* / |-5 + re|------|| + im |------| |
| / | | 3|| | 3| / | | 3|| | 3| |
\ \/ \ \5 + y // \5 + y / \/ \ \5 + y // \5 + y / /
$$\sqrt{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2} - 10 \operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2} + 25} \left(\frac{3 i \left(\sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)} + \frac{\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}}{\sqrt{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}}}\right)}{4} - i \sin^{3}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)} + \cos^{3}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)} - \frac{3 \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)},\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5 \right)}}{3} \right)}}{4} + \frac{3 \operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)}}{4 \sqrt{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}}} - \frac{15}{4 \sqrt{\left(\operatorname{re}{\left(\frac{e^{c}}{y^{3} + 5}\right)} - 5\right)^{2} + \left(\operatorname{im}{\left(\frac{e^{c}}{y^{3} + 5}\right)}\right)^{2}}}\right)$$
sqrt(25 + im(exp(c)/(5 + y^3))^2 + re(exp(c)/(5 + y^3))^2 - 10*re(exp(c)/(5 + y^3)))*(cos(atan2(im(exp(c)/(5 + y^3)), -5 + re(exp(c)/(5 + y^3)))/3)^3 - 15/(4*sqrt((-5 + re(exp(c)/(5 + y^3)))^2 + im(exp(c)/(5 + y^3))^2)) - 3*cos(atan2(im(exp(c)/(5 + y^3)), -5 + re(exp(c)/(5 + y^3)))/3)/4 - i*sin(atan2(im(exp(c)/(5 + y^3)), -5 + re(exp(c)/(5 + y^3)))/3)^3 + 3*i*(im(exp(c)/(5 + y^3))/sqrt((-5 + re(exp(c)/(5 + y^3)))^2 + im(exp(c)/(5 + y^3))^2) + sin(atan2(im(exp(c)/(5 + y^3)), -5 + re(exp(c)/(5 + y^3)))/3))/4 + 3*re(exp(c)/(5 + y^3))/(4*sqrt((-5 + re(exp(c)/(5 + y^3)))^2 + im(exp(c)/(5 + y^3))^2)))