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Derivada de:
Derivada de e^x*sin(x)
Derivada de 5^10
Derivada de 2*cos(3*x)
Derivada de 1/t
Expresiones idénticas
y=(uno +x^(uno / tres))^sin2x
y es igual a (1 más x en el grado (1 dividir por 3)) en el grado seno de 2x
y es igual a (uno más x en el grado (uno dividir por tres)) en el grado seno de 2x
y=(1+x(1/3))sin2x
y=1+x1/3sin2x
y=1+x^1/3^sin2x
y=(1+x^(1 dividir por 3))^sin2x
Expresiones semejantes
y=(1-x^(1/3))^sin2x

Derivada de la función/ sin2x/ x^(1/3)/ y=(1+x^(1/3))^sin2x

Derivada de y=(1+x^(1/3))^sin2x

Solución

Ha introducido [src]

           sin(2*x)
/    3 ___\        
\1 + \/ x /

\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}}

(1 + x^(1/3))^sin(2*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

           sin(2*x)                                                 
/    3 ___\         /              /    3 ___\        sin(2*x)     \
\1 + \/ x /        *|2*cos(2*x)*log\1 + \/ x / + ------------------|
                    |                               2/3 /    3 ___\|
                    \                            3*x   *\1 + \/ x //

\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}} \left(2 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{3 x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right)

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Segunda derivada [src]

                    /                                              2                                                                                            \
                    |/              /    3 ___\       sin(2*x)    \                                                                                             |
                    ||6*cos(2*x)*log\1 + \/ x / + ----------------|                                                                                             |
           sin(2*x) ||                             2/3 /    3 ___\|                                                                                             |
/    3 ___\         |\                            x   *\1 + \/ x //         /    3 ___\                2*sin(2*x)             sin(2*x)            4*cos(2*x)    |
\1 + \/ x /        *|----------------------------------------------- - 4*log\1 + \/ x /*sin(2*x) - ------------------ - ------------------- + ------------------|
                    |                       9                                                         5/3 /    3 ___\                     2      2/3 /    3 ___\|
                    |                                                                              9*x   *\1 + \/ x /      4/3 /    3 ___\    3*x   *\1 + \/ x /|
                    \                                                                                                   9*x   *\1 + \/ x /                      /

\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{\left(6 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right)^{2}}{9} - 4 \log{\left(\sqrt[3]{x} + 1 \right)} \sin{\left(2 x \right)} + \frac{4 \cos{\left(2 x \right)}}{3 x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)} - \frac{\sin{\left(2 x \right)}}{9 x^{\frac{4}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} - \frac{2 \sin{\left(2 x \right)}}{9 x^{\frac{5}{3}} \left(\sqrt[3]{x} + 1\right)}\right)

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Tercera derivada [src]

                    /                                              3                               /              /    3 ___\       sin(2*x)    \ /      /    3 ___\                 sin(2*x)         12*cos(2*x)         2*sin(2*x)   \                                                                                                                               \
                    |/              /    3 ___\       sin(2*x)    \                                |6*cos(2*x)*log\1 + \/ x / + ----------------|*|36*log\1 + \/ x /*sin(2*x) + ----------------- - ---------------- + ----------------|                                                                                                                               |
                    ||6*cos(2*x)*log\1 + \/ x / + ----------------|                                |                             2/3 /    3 ___\| |                                             2    2/3 /    3 ___\    5/3 /    3 ___\|                                                                                                                               |
           sin(2*x) ||                             2/3 /    3 ___\|                                \                            x   *\1 + \/ x // |                              4/3 /    3 ___\    x   *\1 + \/ x /   x   *\1 + \/ x /|                                                                                                                               |
/    3 ___\         |\                            x   *\1 + \/ x //                  /    3 ___\                                                  \                             x   *\1 + \/ x /                                       /      4*sin(2*x)          4*cos(2*x)            2*cos(2*x)            2*sin(2*x)           2*sin(2*x)           10*sin(2*x)    |
\1 + \/ x /        *|----------------------------------------------- - 8*cos(2*x)*log\1 + \/ x / - ------------------------------------------------------------------------------------------------------------------------------------- - ---------------- - ------------------ - ------------------- + ------------------- + ------------------ + -------------------|
                    |                       27                                                                                                                       9                                                                      2/3 /    3 ___\      5/3 /    3 ___\                     2                     2                    3       8/3 /    3 ___\|
                    |                                                                                                                                                                                                                      x   *\1 + \/ x /   3*x   *\1 + \/ x /      4/3 /    3 ___\       7/3 /    3 ___\        2 /    3 ___\    27*x   *\1 + \/ x /|
                    \                                                                                                                                                                                                                                                              3*x   *\1 + \/ x /    9*x   *\1 + \/ x /    27*x *\1 + \/ x /                       /

\left(\sqrt[3]{x} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{\left(6 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right)^{3}}{27} - \frac{\left(6 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)}\right) \left(36 \log{\left(\sqrt[3]{x} + 1 \right)} \sin{\left(2 x \right)} - \frac{12 \cos{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)} + \frac{\sin{\left(2 x \right)}}{x^{\frac{4}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} + \frac{2 \sin{\left(2 x \right)}}{x^{\frac{5}{3}} \left(\sqrt[3]{x} + 1\right)}\right)}{9} - 8 \log{\left(\sqrt[3]{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{2 \sin{\left(2 x \right)}}{27 x^{2} \left(\sqrt[3]{x} + 1\right)^{3}} - \frac{4 \sin{\left(2 x \right)}}{x^{\frac{2}{3}} \left(\sqrt[3]{x} + 1\right)} - \frac{2 \cos{\left(2 x \right)}}{3 x^{\frac{4}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} - \frac{4 \cos{\left(2 x \right)}}{3 x^{\frac{5}{3}} \left(\sqrt[3]{x} + 1\right)} + \frac{2 \sin{\left(2 x \right)}}{9 x^{\frac{7}{3}} \left(\sqrt[3]{x} + 1\right)^{2}} + \frac{10 \sin{\left(2 x \right)}}{27 x^{\frac{8}{3}} \left(\sqrt[3]{x} + 1\right)}\right)

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Gráfico

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Expresiones semejantes

Derivada de y=(1+x^(1/3))^sin2x

Gráfico:

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Solución