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- Derivada de una función implícitamente dada
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- Derivada de:
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Derivada de x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- xtg(((5sqrt(x)+ uno)^ dos - uno)/(5sqrt(x)+ uno))*exp(-x)
- xtg(((5 raíz cuadrada de (x) más 1) al cuadrado menos 1) dividir por (5 raíz cuadrada de (x) más 1)) multiplicar por exponente de ( menos x)
- xtg(((5 raíz cuadrada de (x) más uno) en el grado dos menos uno) dividir por (5 raíz cuadrada de (x) más uno)) multiplicar por exponente de ( menos x)
- xtg(((5√(x)+1)^2-1)/(5√(x)+1))*exp(-x)
- xtg(((5sqrt(x)+1)2-1)/(5sqrt(x)+1))*exp(-x)
- xtg5sqrtx+12-1/5sqrtx+1*exp-x
- xtg(((5sqrt(x)+1)²-1)/(5sqrt(x)+1))*exp(-x)
- xtg(((5sqrt(x)+1) en el grado 2-1)/(5sqrt(x)+1))*exp(-x)
- xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))exp(-x)
- xtg(((5sqrt(x)+1)2-1)/(5sqrt(x)+1))exp(-x)
- xtg5sqrtx+12-1/5sqrtx+1exp-x
- xtg5sqrtx+1^2-1/5sqrtx+1exp-x
- xtg(((5sqrt(x)+1)^2-1) dividir por (5sqrt(x)+1))*exp(-x)
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Expresiones semejantes
- xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))*exp(x)
- xtg(((5sqrt(x)-1)^2-1)/(5sqrt(x)+1))*exp(-x)
- xtg(((5sqrt(x)+1)^2+1)/(5sqrt(x)+1))*exp(-x)
- xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)-1))*exp(-x)
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Expresiones con funciones
- xtg
- xtg|x|
- xtg4x
- xtg2x
- xtg(x+3)
- xtgx(4x-1)
Derivada de xtg(((5sqrt(x)+1)^2-1)/(5sqrt(x)+1))*exp(-x)
Solución
Ha introducido
[src]
/ 2 \
|/ ___ \ |
|\5*\/ x + 1/ - 1| -x
x*tan|------------------|*e
| ___ |
\ 5*\/ x + 1 /
$$x \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} e^{- x}$$
(x*tan(((5*sqrt(x) + 1)^2 - 1)/(5*sqrt(x) + 1)))*exp(-x)
Primera derivada
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/ / / 2 \\ / / 2 \\ / 2 \\ / 2 \ | | |/ ___ \ || | |/ ___ \ || |/ ___ \ || |/ ___ \ | | | 2|\5*\/ x + 1/ - 1|| | 5 5*\\5*\/ x + 1/ - 1/| |\5*\/ x + 1/ - 1|| -x -x |\5*\/ x + 1/ - 1| |x*|1 + tan |------------------||*|----- - ----------------------| + tan|------------------||*e - x*e *tan|------------------| | | | ___ || | ___ 2| | ___ || | ___ | | \ \ 5*\/ x + 1 // |\/ x ___ / ___ \ | \ 5*\/ x + 1 /| \ 5*\/ x + 1 / \ \ 2*\/ x *\5*\/ x + 1/ / /
$$- x e^{- x} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + \left(x \left(\frac{5}{\sqrt{x}} - \frac{5 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{2 \sqrt{x} \left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right) + \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}\right) e^{- x}$$
Segunda derivada
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/ / / 2 \ \ \ | | | / 2\ / 2\| / 2\| | | | | | / ___\ | | / ___\ || | / ___\ || | | | | | -1 + \1 + 5*\/ x / | |-1 + \1 + 5*\/ x / || | -1 + \1 + 5*\/ x / || | | | | 10*|2 - -------------------| *tan|-------------------|| 4*|2 - -------------------|| | | / / 2\\ | | 2 / 2\ | 2 | | ___ || | 2 || | | | | / ___\ || | | / ___\ | / ___\ | | / ___\ | \ 1 + 5*\/ x /| | / ___\ || | | | 2|-1 + \1 + 5*\/ x / || | | 2 10 -1 + \1 + 5*\/ x / 10*\-1 + \1 + 5*\/ x / / \ \1 + 5*\/ x / / | \ \1 + 5*\/ x / /| | | 5*|1 + tan |-------------------||*|x*|- ---- - --------------- + ------------------- + ------------------------ + ------------------------------------------------------| + ---------------------------| | | / 2\ / 2\ | | ___ || | | 3/2 / ___\ 2 3 x | ___ | / / 2\\ / 2\| | | / ___\ | | / ___\ | \ \ 1 + 5*\/ x // | | x x*\1 + 5*\/ x / 3/2 / ___\ / ___\ | \/ x | | | / ___\ || | / ___\ || | |-1 + \1 + 5*\/ x / | |-1 + \1 + 5*\/ x / | \ \ x *\1 + 5*\/ x / x*\1 + 5*\/ x / / / ___ | 2|-1 + \1 + 5*\/ x / || | -1 + \1 + 5*\/ x / || -x |- 2*tan|-------------------| + x*tan|-------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - 5*\/ x *|1 + tan |-------------------||*|2 - -------------------||*e | | ___ | | ___ | 4 | | ___ || | 2 || | \ 1 + 5*\/ x / \ 1 + 5*\/ x / \ \ 1 + 5*\/ x // | / ___\ || \ \ \1 + 5*\/ x / //
$$\left(- 5 \sqrt{x} \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right) + x \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + \frac{5 \left(x \left(\frac{10 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{2} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x} - \frac{10}{x \left(5 \sqrt{x} + 1\right)} + \frac{10 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} - \frac{2}{x^{\frac{3}{2}}} + \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) + \frac{4 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)}{\sqrt{x}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{4} - 2 \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}\right) e^{- x}$$
Tercera derivada
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/ / / 2 \ \ / / 3 3 \ 2 \ \ | | | / 2\ / 2\| / 2\| | | / 2\ / / 2\\ / 2\ / 2\ / 2\ / 2 / 2\\ / 2\| / 2\ / 2\| | | | | | / ___\ | | / ___\ || | / ___\ || | | | / ___\ | | | / ___\ || | / ___\ | | / ___\ | | / ___\ | | / ___\ | / ___\ || | / ___\ || | / ___\ | | / ___\ || | | | | | -1 + \1 + 5*\/ x / | |-1 + \1 + 5*\/ x / || | -1 + \1 + 5*\/ x / || | | | -1 + \1 + 5*\/ x / | | 2|-1 + \1 + 5*\/ x / || | -1 + \1 + 5*\/ x / | 2|-1 + \1 + 5*\/ x / | | -1 + \1 + 5*\/ x / | | 2 10 -1 + \1 + 5*\/ x / 10*\-1 + \1 + 5*\/ x / /| |-1 + \1 + 5*\/ x / || | -1 + \1 + 5*\/ x / | |-1 + \1 + 5*\/ x / || | | | | 10*|2 - -------------------| *tan|-------------------|| 4*|2 - -------------------|| | | 50*|2 - -------------------| *|1 + tan |-------------------|| 100*|2 - -------------------| *tan |-------------------| 30*|2 - -------------------|*|---- + --------------- - ------------------- - ------------------------|*tan|-------------------|| 60*|2 - -------------------| *tan|-------------------|| | | / / 2\\ | | 2 / 2\ | 2 | | ___ || | 2 || / / 2\\ | | / 2\ / 2\ / 2\ | 2 | | | ___ || | 2 | | ___ | | 2 | | 3/2 / ___\ 2 3 | | ___ || / 2\ / 2\ | 2 | | ___ || / / 2\\ / 2\| | | | / ___\ || | | / ___\ | / ___\ | | / ___\ | \ 1 + 5*\/ x /| | / ___\ || | | / ___\ || | | | / ___\ | | / ___\ | | / ___\ | | / ___\ | \ \ 1 + 5*\/ x // | / ___\ | \ 1 + 5*\/ x / | / ___\ | |x x*\1 + 5*\/ x / 3/2 / ___\ / ___\ | \ 1 + 5*\/ x /| | / ___\ | | / ___\ | | / ___\ | \ 1 + 5*\/ x /| | | / ___\ || | / ___\ || | | 2|-1 + \1 + 5*\/ x / || | | 2 10 -1 + \1 + 5*\/ x / 10*\-1 + \1 + 5*\/ x / / \ \1 + 5*\/ x / / | \ \1 + 5*\/ x / /| | 2|-1 + \1 + 5*\/ x / || | 12 | 6 30 150 150*\-1 + \1 + 5*\/ x / / 30*\-1 + \1 + 5*\/ x / / 3*\-1 + \1 + 5*\/ x / / \ \1 + 5*\/ x / / \ \1 + 5*\/ x / / \ \1 + 5*\/ x / / \ x *\1 + 5*\/ x / x*\1 + 5*\/ x / / | 60 6*\-1 + \1 + 5*\/ x / / 60*\-1 + \1 + 5*\/ x / / \ \1 + 5*\/ x / / | ___ | 2|-1 + \1 + 5*\/ x / || | -1 + \1 + 5*\/ x / || | 15*|1 + tan |-------------------||*|x*|- ---- - --------------- + ------------------- + ------------------------ + ------------------------------------------------------| + ---------------------------| 5*|1 + tan |-------------------||*|- ---- + x*|---- + ---------------- + ------------------- - ------------------------- - ------------------------ - ----------------------- + ------------------------------------------------------------- + -------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------| - --------------- + ----------------------- + ------------------------ + ------------------------------------------------------| 15*\/ x *|1 + tan |-------------------||*|2 - -------------------|| | / 2\ / 2\ | | ___ || | | 3/2 / ___\ 2 3 x | ___ | | | ___ || | 3/2 | 5/2 2 / ___\ 2 4 3 2 3/2 3/2 ___ | / ___\ 2 3 x | | | ___ || | 2 || | | / ___\ | | / ___\ | \ \ 1 + 5*\/ x // | | x x*\1 + 5*\/ x / 3/2 / ___\ / ___\ | \/ x | \ \ 1 + 5*\/ x // | x |x x *\1 + 5*\/ x / 3/2 / ___\ 3/2 / ___\ 2 / ___\ 5/2 / ___\ x x \/ x | x*\1 + 5*\/ x / 3/2 / ___\ / ___\ | \ \ 1 + 5*\/ x // | / ___\ || | |-1 + \1 + 5*\/ x / | |-1 + \1 + 5*\/ x / | \ \ x *\1 + 5*\/ x / x*\1 + 5*\/ x / / / \ \ x *\1 + 5*\/ x / x *\1 + 5*\/ x / x *\1 + 5*\/ x / x *\1 + 5*\/ x / / x *\1 + 5*\/ x / x*\1 + 5*\/ x / / \ \1 + 5*\/ x / /| -x |3*tan|-------------------| - x*tan|-------------------| - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------|*e | | ___ | | ___ | 4 8 2 | \ \ 1 + 5*\/ x / \ 1 + 5*\/ x / /
$$\left(\frac{15 \sqrt{x} \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{2} - x \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} - \frac{15 \left(x \left(\frac{10 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{2} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x} - \frac{10}{x \left(5 \sqrt{x} + 1\right)} + \frac{10 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} - \frac{2}{x^{\frac{3}{2}}} + \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) + \frac{4 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)}{\sqrt{x}}\right) \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{4} + \frac{5 \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right) \left(x \left(\frac{30}{x^{2} \left(5 \sqrt{x} + 1\right)} - \frac{30 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{2} \left(5 \sqrt{x} + 1\right)^{3}} - \frac{30 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right) \left(\frac{10}{x \left(5 \sqrt{x} + 1\right)} - \frac{10 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} + \frac{2}{x^{\frac{3}{2}}} - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{\sqrt{x}} + \frac{50 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{3} \left(\tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{100 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{3} \tan^{2}{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x^{\frac{3}{2}}} + \frac{150}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}} - \frac{150 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{4}} + \frac{6}{x^{\frac{5}{2}}} - \frac{3 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{\frac{5}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right) + \frac{60 \left(2 - \frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{\left(5 \sqrt{x} + 1\right)^{2}}\right)^{2} \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}}{x} - \frac{60}{x \left(5 \sqrt{x} + 1\right)} + \frac{60 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x \left(5 \sqrt{x} + 1\right)^{3}} - \frac{12}{x^{\frac{3}{2}}} + \frac{6 \left(\left(5 \sqrt{x} + 1\right)^{2} - 1\right)}{x^{\frac{3}{2}} \left(5 \sqrt{x} + 1\right)^{2}}\right)}{8} + 3 \tan{\left(\frac{\left(5 \sqrt{x} + 1\right)^{2} - 1}{5 \sqrt{x} + 1} \right)}\right) e^{- x}$$
Gráfico