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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de 1/x^(1/2)
Derivada de x^-(4/5)
Expresiones idénticas
y=(x^ cinco + uno)^ctgx
y es igual a (x en el grado 5 más 1) en el grado ctgx
y es igual a (x en el grado cinco más uno) en el grado ctgx
y=(x5+1)ctgx
y=x5+1ctgx
y=(x⁵+1)^ctgx
y=x^5+1^ctgx
Expresiones semejantes
y=(x^5-1)^ctgx

Derivada de la función/ x^5+1/ y=(x^5+1)^ctgx

Derivada de y=(x^5+1)^ctgx

Solución

Ha introducido [src]

        cot(x)
/ 5    \      
\x  + 1/

\left(x^{5} + 1\right)^{\cot{\left(x \right)}}

(x^5 + 1)^cot(x)

Solución detallada

No logro encontrar los pasos en la búsqueda de esta derivada.

Perola derivada

$\left(\log{\left(\cot{\left(x \right)} \right)} + 1\right) \cot^{\cot{\left(x \right)}}{\left(x \right)}$

Respuesta:

$\left(\log{\left(\cot{\left(x \right)} \right)} + 1\right) \cot^{\cot{\left(x \right)}}{\left(x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

        cot(x) /                                4       \
/ 5    \       |/        2   \    / 5    \   5*x *cot(x)|
\x  + 1/      *|\-1 - cot (x)/*log\x  + 1/ + -----------|
               |                                 5      |
               \                                x  + 1  /

\left(x^{5} + 1\right)^{\cot{\left(x \right)}} \left(\frac{5 x^{4} \cot{\left(x \right)}}{x^{5} + 1} + \left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(x^{5} + 1 \right)}\right)

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Segunda derivada [src]

               /                                           2                                                                                         \
        cot(x) |/                                 4       \        8              4 /       2   \                                            3       |
/     5\       ||  /       2   \    /     5\   5*x *cot(x)|    25*x *cot(x)   10*x *\1 + cot (x)/     /       2   \           /     5\   20*x *cot(x)|
\1 + x /      *||- \1 + cot (x)/*log\1 + x / + -----------|  - ------------ - ------------------- + 2*\1 + cot (x)/*cot(x)*log\1 + x / + ------------|
               ||                                      5  |             2                 5                                                      5   |
               |\                                 1 + x   /     /     5\             1 + x                                                  1 + x    |
               \                                                \1 + x /                                                                             /

\left(x^{5} + 1\right)^{\cot{\left(x \right)}} \left(- \frac{25 x^{8} \cot{\left(x \right)}}{\left(x^{5} + 1\right)^{2}} - \frac{10 x^{4} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{5} + 1} + \frac{20 x^{3} \cot{\left(x \right)}}{x^{5} + 1} + \left(\frac{5 x^{4} \cot{\left(x \right)}}{x^{5} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{5} + 1 \right)}\right)^{2} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{5} + 1 \right)} \cot{\left(x \right)}\right)

Simplificar

Tercera derivada [src]

               /                                           3                                                                                                                                                                                                                                                                                                                                         \
        cot(x) |/                                 4       \      /                                 4       \ /      3                                                   4 /       2   \       8       \                  2                    7              3 /       2   \                                             2              8 /       2   \        12              4 /       2   \       |
/     5\       ||  /       2   \    /     5\   5*x *cot(x)|      |  /       2   \    /     5\   5*x *cot(x)| |  20*x *cot(x)     /       2   \           /     5\   10*x *\1 + cot (x)/   25*x *cot(x)|     /       2   \     /     5\   300*x *cot(x)   60*x *\1 + cot (x)/        2    /       2   \    /     5\   60*x *cot(x)   75*x *\1 + cot (x)/   250*x  *cot(x)   30*x *\1 + cot (x)/*cot(x)|
\1 + x /      *||- \1 + cot (x)/*log\1 + x / + -----------|  - 3*|- \1 + cot (x)/*log\1 + x / + -----------|*|- ------------ - 2*\1 + cot (x)/*cot(x)*log\1 + x / + ------------------- + ------------| - 2*\1 + cot (x)/ *log\1 + x / - ------------- - ------------------- - 4*cot (x)*\1 + cot (x)/*log\1 + x / + ------------ + ------------------- + -------------- + --------------------------|
               ||                                      5  |      |                                      5  | |          5                                                       5                  2  |                                            2                 5                                                       5                   2                  3                     5          |
               |\                                 1 + x   /      \                                 1 + x   / |     1 + x                                                   1 + x           /     5\   |                                    /     5\             1 + x                                                   1 + x            /     5\           /     5\                 1 + x           |
               \                                                                                             \                                                                             \1 + x /   /                                    \1 + x /                                                                                      \1 + x /           \1 + x /                                 /

\left(x^{5} + 1\right)^{\cot{\left(x \right)}} \left(\frac{250 x^{12} \cot{\left(x \right)}}{\left(x^{5} + 1\right)^{3}} + \frac{75 x^{8} \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(x^{5} + 1\right)^{2}} - \frac{300 x^{7} \cot{\left(x \right)}}{\left(x^{5} + 1\right)^{2}} + \frac{30 x^{4} \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x^{5} + 1} - \frac{60 x^{3} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{5} + 1} + \frac{60 x^{2} \cot{\left(x \right)}}{x^{5} + 1} + \left(\frac{5 x^{4} \cot{\left(x \right)}}{x^{5} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{5} + 1 \right)}\right)^{3} - 3 \left(\frac{5 x^{4} \cot{\left(x \right)}}{x^{5} + 1} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{5} + 1 \right)}\right) \left(\frac{25 x^{8} \cot{\left(x \right)}}{\left(x^{5} + 1\right)^{2}} + \frac{10 x^{4} \left(\cot^{2}{\left(x \right)} + 1\right)}{x^{5} + 1} - \frac{20 x^{3} \cot{\left(x \right)}}{x^{5} + 1} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{5} + 1 \right)} \cot{\left(x \right)}\right) - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{5} + 1 \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x^{5} + 1 \right)} \cot^{2}{\left(x \right)}\right)

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Gráfico

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Expresiones idénticas

Expresiones semejantes

Derivada de y=(x^5+1)^ctgx

Gráfico:

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