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Derivada de e^x+x^2
Derivada de -e^x
Derivada de x^2sinx
Derivada de x^(1/3)/(3*x+2)
Expresiones idénticas
y=(cos(sqrt(x)))^(tg(7x))
y es igual a ( coseno de ( raíz cuadrada de (x))) en el grado (tg(7x))
y=(cos(√(x)))^(tg(7x))
y=(cos(sqrt(x)))(tg(7x))
y=cossqrtxtg7x
y=cossqrtx^tg7x
Expresiones con funciones
Coseno cos
cos(x^2+1)
cos(3*x+1)
cos(x)/2
cos(4*(x^2)-sqrt(x))
cos(3)^(2)*x
Raíz cuadrada sqrt
sqrt3(x^2)
sqrt(x²+1)
sqrt(x)/x
sqrtlnx
sqrt(x*3)
tg
tg(x^3)
tg5x^1/5
tg(x)^3
tgx-9x
tg^3(2x)

Derivada de la función/ tg(7x)/ sqrt(x)/ y=(cos(sqrt(x)))^(tg(7x))

Derivada de y=(cos(sqrt(x)))^(tg(7x))

Solución

Ha introducido [src]

   tan(7*x)/  ___\
cos        \\/ x /

\cos^{\tan{\left(7 x \right)}}{\left(\sqrt{x} \right)}

cos(sqrt(x))^tan(7*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\tan{\left(7 x \right)} \right)} + 1\right) \tan^{\tan{\left(7 x \right)}}{\left(7 x \right)}$

Respuesta:

$\left(\log{\left(\tan{\left(7 x \right)} \right)} + 1\right) \tan^{\tan{\left(7 x \right)}}{\left(7 x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                   /                                       /  ___\         \
   tan(7*x)/  ___\ |/         2     \    /   /  ___\\   sin\\/ x /*tan(7*x)|
cos        \\/ x /*|\7 + 7*tan (7*x)/*log\cos\\/ x // - -------------------|
                   |                                         ___    /  ___\|
                   \                                     2*\/ x *cos\\/ x //

\left(\left(7 \tan^{2}{\left(7 x \right)} + 7\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} - \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{2 \sqrt{x} \cos{\left(\sqrt{x} \right)}}\right) \cos^{\tan{\left(7 x \right)}}{\left(\sqrt{x} \right)}

Simplificar

Segunda derivada [src]

                   /                                                          2                                                                                                                                     \
                   |/                                        /  ___\         \                                                                                                                                      |
                   ||   /       2     \    /   /  ___\\   sin\\/ x /*tan(7*x)|                                                                                                                                      |
                   ||14*\1 + tan (7*x)/*log\cos\\/ x // - -------------------|                                                                                                                                      |
                   ||                                         ___    /  ___\ |                                                               /       2     \    /  ___\      2/  ___\               /  ___\         |
   tan(7*x)/  ___\ |\                                       \/ x *cos\\/ x / /    tan(7*x)      /       2     \    /   /  ___\\            7*\1 + tan (7*x)/*sin\\/ x /   sin \\/ x /*tan(7*x)   sin\\/ x /*tan(7*x)|
cos        \\/ x /*|----------------------------------------------------------- - -------- + 98*\1 + tan (7*x)/*log\cos\\/ x //*tan(7*x) - ---------------------------- - -------------------- + -------------------|
                   |                             4                                  4*x                                                            ___    /  ___\                  2/  ___\          3/2    /  ___\ |
                   \                                                                                                                             \/ x *cos\\/ x /           4*x*cos \\/ x /       4*x   *cos\\/ x / /

\left(\frac{\left(14 \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} - \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{\sqrt{x} \cos{\left(\sqrt{x} \right)}}\right)^{2}}{4} + 98 \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} \tan{\left(7 x \right)} - \frac{\sin^{2}{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{4 x \cos^{2}{\left(\sqrt{x} \right)}} - \frac{\tan{\left(7 x \right)}}{4 x} - \frac{7 \left(\tan^{2}{\left(7 x \right)} + 1\right) \sin{\left(\sqrt{x} \right)}}{\sqrt{x} \cos{\left(\sqrt{x} \right)}} + \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{4 x^{\frac{3}{2}} \cos{\left(\sqrt{x} \right)}}\right) \cos^{\tan{\left(7 x \right)}}{\left(\sqrt{x} \right)}

Simplificar

Tercera derivada [src]

                   /                                                          3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \
                   |/                                        /  ___\         \                                                                  /                                        /  ___\         \ /                                                             2/  ___\               /  ___\               /       2     \    /  ___\\                                                                                                                                                                                                                                                                       |
                   ||   /       2     \    /   /  ___\\   sin\\/ x /*tan(7*x)|                                                                  |   /       2     \    /   /  ___\\   sin\\/ x /*tan(7*x)| |tan(7*x)       /       2     \    /   /  ___\\            sin \\/ x /*tan(7*x)   sin\\/ x /*tan(7*x)   28*\1 + tan (7*x)/*sin\\/ x /|                                                                                                                                                                                                                                                                       |
                   ||14*\1 + tan (7*x)/*log\cos\\/ x // - -------------------|                                                                3*|14*\1 + tan (7*x)/*log\cos\\/ x // - -------------------|*|-------- - 392*\1 + tan (7*x)/*log\cos\\/ x //*tan(7*x) + -------------------- - ------------------- + -----------------------------|                                                                                                                                                                                                                                                                       |
                   ||                                         ___    /  ___\ |                       2                      /       2     \     |                                         ___    /  ___\ | |   x                                                              2/  ___\          3/2    /  ___\              ___    /  ___\      |                                                                       2/  ___\ /       2     \        /  ___\               /  ___\               3/  ___\                 2/  ___\               /       2     \    /  ___\       /       2     \    /  ___\         |
   tan(7*x)/  ___\ |\                                       \/ x *cos\\/ x / /        /       2     \     /   /  ___\\   21*\1 + tan (7*x)/     \                                       \/ x *cos\\/ x / / \                                                             x*cos \\/ x /         x   *cos\\/ x /            \/ x *cos\\/ x /      /   3*tan(7*x)           2      /       2     \    /   /  ___\\   21*sin \\/ x /*\1 + tan (7*x)/   3*sin\\/ x /*tan(7*x)   sin\\/ x /*tan(7*x)   sin \\/ x /*tan(7*x)   3*sin \\/ x /*tan(7*x)   21*\1 + tan (7*x)/*sin\\/ x /   147*\1 + tan (7*x)/*sin\\/ x /*tan(7*x)|
cos        \\/ x /*|----------------------------------------------------------- + 686*\1 + tan (7*x)/ *log\cos\\/ x // - ------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------- + 1372*tan (7*x)*\1 + tan (7*x)/*log\cos\\/ x // - ------------------------------ - --------------------- - ------------------- - -------------------- + ---------------------- + ----------------------------- - ---------------------------------------|
                   |                             8                                                                              4*x                                                                                                            8                                                                                                          2                                                                     2/  ___\                5/2    /  ___\         3/2    /  ___\        3/2    3/  ___\          2    2/  ___\               3/2    /  ___\                       ___    /  ___\           |
                   \                                                                                                                                                                                                                                                                                                                                   8*x                                                               4*x*cos \\/ x /             8*x   *cos\\/ x /      4*x   *cos\\/ x /     4*x   *cos \\/ x /       8*x *cos \\/ x /            4*x   *cos\\/ x /                     \/ x *cos\\/ x /           /

\left(\frac{\left(14 \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} - \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{\sqrt{x} \cos{\left(\sqrt{x} \right)}}\right)^{3}}{8} - \frac{3 \left(14 \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} - \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{\sqrt{x} \cos{\left(\sqrt{x} \right)}}\right) \left(- 392 \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} \tan{\left(7 x \right)} + \frac{\sin^{2}{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{x \cos^{2}{\left(\sqrt{x} \right)}} + \frac{\tan{\left(7 x \right)}}{x} + \frac{28 \left(\tan^{2}{\left(7 x \right)} + 1\right) \sin{\left(\sqrt{x} \right)}}{\sqrt{x} \cos{\left(\sqrt{x} \right)}} - \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{x^{\frac{3}{2}} \cos{\left(\sqrt{x} \right)}}\right)}{8} + 686 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2} \log{\left(\cos{\left(\sqrt{x} \right)} \right)} + 1372 \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\cos{\left(\sqrt{x} \right)} \right)} \tan^{2}{\left(7 x \right)} - \frac{21 \left(\tan^{2}{\left(7 x \right)} + 1\right) \sin^{2}{\left(\sqrt{x} \right)}}{4 x \cos^{2}{\left(\sqrt{x} \right)}} - \frac{21 \left(\tan^{2}{\left(7 x \right)} + 1\right)}{4 x} + \frac{3 \sin^{2}{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{8 x^{2} \cos^{2}{\left(\sqrt{x} \right)}} + \frac{3 \tan{\left(7 x \right)}}{8 x^{2}} - \frac{147 \left(\tan^{2}{\left(7 x \right)} + 1\right) \sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{\sqrt{x} \cos{\left(\sqrt{x} \right)}} + \frac{21 \left(\tan^{2}{\left(7 x \right)} + 1\right) \sin{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \cos{\left(\sqrt{x} \right)}} - \frac{\sin^{3}{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{4 x^{\frac{3}{2}} \cos^{3}{\left(\sqrt{x} \right)}} - \frac{\sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{4 x^{\frac{3}{2}} \cos{\left(\sqrt{x} \right)}} - \frac{3 \sin{\left(\sqrt{x} \right)} \tan{\left(7 x \right)}}{8 x^{\frac{5}{2}} \cos{\left(\sqrt{x} \right)}}\right) \cos^{\tan{\left(7 x \right)}}{\left(\sqrt{x} \right)}

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Gráfico

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Derivada de y=(cos(sqrt(x)))^(tg(7x))

Gráfico:

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Solución