Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de 9/2x
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Derivada de 8*y^3-64
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Derivada de (7x+5)'
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Derivada de (-9)/x^7-15*x^4+28/x^3+35*x^4-7
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Expresiones idénticas
- y=sin^ diez (arcctg(x))/sin^ siete (sqrt(x))+ uno /x^ veintidós
- y es igual a seno de en el grado 10(arcctg(x)) dividir por seno de en el grado 7( raíz cuadrada de (x)) más 1 dividir por x al cuadrado 2
- y es igual a seno de en el grado diez (arcctg(x)) dividir por seno de en el grado siete ( raíz cuadrada de (x)) más uno dividir por x en el grado veintidós
- y=sin^10(arcctg(x))/sin^7(√(x))+1/x^22
- y=sin10(arcctg(x))/sin7(sqrt(x))+1/x22
- y=sin10arcctgx/sin7sqrtx+1/x22
- y=sin^10(arcctg(x))/sin⁷(sqrt(x))+1/x²2
- y=sin en el grado 10(arcctg(x))/sin en el grado 7(sqrt(x))+1/x en el grado 22
- y=sin^10arcctgx/sin^7sqrtx+1/x^22
- y=sin^10(arcctg(x)) dividir por sin^7(sqrt(x))+1 dividir por x^22
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Expresiones semejantes
- y=sin^10(arcctg(x))/sin^7(sqrt(x))-1/x^22
Derivada de y=sin^10(arcctg(x))/sin^7(sqrt(x))+1/x^22
Solución
Ha introducido
[src]
10
sin (acot(x)) 1
-------------- + ---
7/ ___\ 22
sin \\/ x / x
$$\frac{\sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sin^{7}{\left(\sqrt{x} \right)}} + \frac{1}{x^{22}}$$
sin(acot(x))^10/sin(sqrt(x))^7 + 1/(x^22)
Primera derivada
[src]
9 10 / ___\
22 10*sin (acot(x)) 7*sin (acot(x))*cos\\/ x /
- ----- - ---------------------------------- - ---------------------------
22 ________ ___ 8/ ___\
x*x / 1 / 2\ 7/ ___\ 2*\/ x *sin \\/ x /
/ 1 + -- *\1 + x /*sin \\/ x /
/ 2
\/ x
$$- \frac{10 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{22}{x x^{22}} - \frac{7 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 \sqrt{x} \sin^{8}{\left(\sqrt{x} \right)}}$$
Segunda derivada
[src]
10 2/ ___\ 10 8 10 / ___\ 9 9 9 / ___\
506 7*sin (acot(x)) 14*cos \\/ x /*sin (acot(x)) 90*sin (acot(x)) 7*sin (acot(x))*cos\\/ x / 10*sin (acot(x)) 20*x*sin (acot(x)) 70*sin (acot(x))*cos\\/ x /
--- + ---------------- + ----------------------------- + ------------------------------ + --------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------------
24 7/ ___\ 9/ ___\ 2 3/2 8/ ___\ 3/2 ________ 2 ________
x 4*x*sin \\/ x / x*sin \\/ x / / 1 \ / 2\ 7/ ___\ 4*x *sin \\/ x / 3 / 1 \ / 2\ 7/ ___\ / 1 / 2\ 7/ ___\ ___ / 1 / 2\ 8/ ___\
|1 + --|*\1 + x / *sin \\/ x / x *|1 + --| *\1 + x /*sin \\/ x / / 1 + -- *\1 + x / *sin \\/ x / \/ x * / 1 + -- *\1 + x /*sin \\/ x /
| 2| | 2| / 2 / 2
\ x / \ x / \/ x \/ x
$$\frac{20 x \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{90 \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\left(1 + \frac{1}{x^{2}}\right) \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{7 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)}}{4 x \sin^{7}{\left(\sqrt{x} \right)}} + \frac{14 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{9}{\left(\sqrt{x} \right)}} - \frac{10 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{3} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} + \frac{506}{x^{24}} + \frac{70 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{8}{\left(\sqrt{x} \right)}} + \frac{7 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{8}{\left(\sqrt{x} \right)}}$$
Tercera derivada
[src]
10 7 3/ ___\ 10 2/ ___\ 10 9 10 / ___\ 10 / ___\ 8 2 9 9 9 9 8 9 8 / ___\ 2/ ___\ 9 ___ 9 / ___\ 9 / ___\ 9 / ___\
12144 21*sin (acot(x)) 720*sin (acot(x)) 63*cos \\/ x /*sin (acot(x)) 21*cos \\/ x /*sin (acot(x)) 20*sin (acot(x)) 161*sin (acot(x))*cos\\/ x / 21*sin (acot(x))*cos\\/ x / 540*x*sin (acot(x)) 80*x *sin (acot(x)) 30*sin (acot(x)) 30*sin (acot(x)) 40*sin (acot(x)) 270*sin (acot(x)) 105*sin (acot(x)) 945*sin (acot(x))*cos\\/ x / 420*cos \\/ x /*sin (acot(x)) 210*\/ x *sin (acot(x))*cos\\/ x / 105*sin (acot(x))*cos\\/ x / 105*sin (acot(x))*cos\\/ x /
- ----- - ----------------- - --------------------------------- - ----------------------------- - ----------------------------- + ----------------------------------- - ----------------------------- - ---------------------------- - ------------------------------ - ----------------------------------- - ----------------------------------- + ----------------------------------- + ------------------------------------ + ---------------------------------- - -------------------------------------- - ------------------------------------ - ------------------------------------ - ----------------------------------- + ------------------------------------- - -----------------------------------------
25 2 7/ ___\ 3/2 3 3/2 10/ ___\ 2 9/ ___\ ________ 2 3/2 8/ ___\ 5/2 8/ ___\ 3 ________ 3 5/2 3/2 3/2 2 2 2 ________ 2 ________ ________ 2 3/2 ________
x 8*x *sin \\/ x / / 1 \ / 2\ 7/ ___\ x *sin \\/ x / x *sin \\/ x / / 1 / 2\ 7/ ___\ 8*x *sin \\/ x / 8*x *sin \\/ x / / 1 \ / 2\ 7/ ___\ / 1 / 2\ 7/ ___\ 6 / 1 \ / 2\ 7/ ___\ 4 / 1 \ / 2\ 7/ ___\ 2 / 1 \ / 2\ 7/ ___\ 3 / 1 \ / 2\ 7/ ___\ / 1 / 2\ 7/ ___\ ___ / 1 \ / 2\ 8/ ___\ / 1 / 2\ 9/ ___\ / 1 / 2\ 8/ ___\ 7/2 / 1 \ / 2\ 8/ ___\ 3/2 / 1 / 2\ 8/ ___\
|1 + --| *\1 + x / *sin \\/ x / / 1 + -- *\1 + x / *sin \\/ x / |1 + --|*\1 + x / *sin \\/ x / / 1 + -- *\1 + x / *sin \\/ x / x *|1 + --| *\1 + x /*sin \\/ x / x *|1 + --| *\1 + x /*sin \\/ x / x *|1 + --| *\1 + x / *sin \\/ x / x *|1 + --| *\1 + x / *sin \\/ x / 2*x* / 1 + -- *\1 + x /*sin \\/ x / \/ x *|1 + --|*\1 + x / *sin \\/ x / x* / 1 + -- *\1 + x /*sin \\/ x / / 1 + -- *\1 + x / *sin \\/ x / x *|1 + --| *\1 + x /*sin \\/ x / 2*x * / 1 + -- *\1 + x /*sin \\/ x /
| 2| / 2 | 2| / 2 | 2| | 2| | 2| | 2| / 2 | 2| / 2 / 2 | 2| / 2
\ x / \/ x \ x / \/ x \ x / \ x / \ x / \ x / \/ x \ x / \/ x \/ x \ x / \/ x
$$- \frac{210 \sqrt{x} \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{2} \sin^{8}{\left(\sqrt{x} \right)}} - \frac{80 x^{2} \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{3} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{540 x \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\left(1 + \frac{1}{x^{2}}\right) \left(x^{2} + 1\right)^{3} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{20 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{720 \sin^{7}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{3} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{105 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{2 x \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{420 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{9}{\left(\sqrt{x} \right)}} - \frac{21 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)}}{8 x^{2} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{21 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x^{2} \sin^{9}{\left(\sqrt{x} \right)}} + \frac{40 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{270 \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{3} \left(1 + \frac{1}{x^{2}}\right)^{2} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{30 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{4} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{30 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{6} \left(1 + \frac{1}{x^{2}}\right)^{\frac{5}{2}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{12144}{x^{25}} - \frac{945 \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \left(1 + \frac{1}{x^{2}}\right) \left(x^{2} + 1\right)^{2} \sin^{8}{\left(\sqrt{x} \right)}} - \frac{161 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{3}{2}} \sin^{8}{\left(\sqrt{x} \right)}} - \frac{63 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{10}{\left(\sqrt{x} \right)}} - \frac{105 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{8}{\left(\sqrt{x} \right)}} - \frac{21 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{5}{2}} \sin^{8}{\left(\sqrt{x} \right)}} + \frac{105 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{x^{\frac{7}{2}} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \sin^{8}{\left(\sqrt{x} \right)}}$$
Gráfico