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Derivada de x/a
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Expresiones idénticas
y=(uno +(tres)sqrt(x))^sin2x
y es igual a (1 más (3) raíz cuadrada de (x)) en el grado seno de 2x
y es igual a (uno más (tres) raíz cuadrada de (x)) en el grado seno de 2x
y=(1+(3)√(x))^sin2x
y=(1+(3)sqrt(x))sin2x
y=1+3sqrtxsin2x
y=1+3sqrtx^sin2x
Expresiones semejantes
y=(1-(3)sqrt(x))^sin2x
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x^2+16)+3x
sqrt(1)+x^2
sqrt((x-1)/2)
sqrt(acos(1-(1)/x))^(3)
sqrt(1-x^2)+acos(x)

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

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

Solución

Ha introducido [src]

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

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

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

                      /                                                   3                                   /              /        ___\        3*sin(2*x)    \ /      /        ___\                24*cos(2*x)           3*sin(2*x)          9*sin(2*x)   \                                                                                                                                       \
                      |/              /        ___\        3*sin(2*x)    \                                  3*|4*cos(2*x)*log\1 + 3*\/ x / + -------------------|*|16*log\1 + 3*\/ x /*sin(2*x) - ------------------- + ------------------ + ----------------|                                                                                                                                       |
                      ||4*cos(2*x)*log\1 + 3*\/ x / + -------------------|                                    |                                ___ /        ___\| |                                 ___ /        ___\    3/2 /        ___\                  2|                                                                                                                                       |
             sin(2*x) ||                                ___ /        ___\|                                    \                              \/ x *\1 + 3*\/ x // |                               \/ x *\1 + 3*\/ x /   x   *\1 + 3*\/ x /     /        ___\ |                                                                                                                                       |
/        ___\         |\                              \/ x *\1 + 3*\/ x //                  /        ___\                                                         \                                                                          x*\1 + 3*\/ x / /       18*sin(2*x)          27*cos(2*x)            9*cos(2*x)             9*sin(2*x)             27*sin(2*x)            27*sin(2*x)    |
\1 + 3*\/ x /        *|---------------------------------------------------- - 8*cos(2*x)*log\1 + 3*\/ x / - -------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------- - ------------------ - -------------------- + -------------------- + --------------------- + -------------------|
                      |                         8                                                                                                                                   8                                                                              ___ /        ___\                    2      3/2 /        ___\      5/2 /        ___\                       3                     2|
                      |                                                                                                                                                                                                                                          \/ x *\1 + 3*\/ x /       /        ___\    2*x   *\1 + 3*\/ x /   8*x   *\1 + 3*\/ x /      3/2 /        ___\       2 /        ___\ |
                      \                                                                                                                                                                                                                                                                2*x*\1 + 3*\/ x /                                                  4*x   *\1 + 3*\/ x /    8*x *\1 + 3*\/ x / /

\left(3 \sqrt{x} + 1\right)^{\sin{\left(2 x \right)}} \left(\frac{\left(4 \log{\left(3 \sqrt{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{3 \sin{\left(2 x \right)}}{\sqrt{x} \left(3 \sqrt{x} + 1\right)}\right)^{3}}{8} - \frac{3 \left(4 \log{\left(3 \sqrt{x} + 1 \right)} \cos{\left(2 x \right)} + \frac{3 \sin{\left(2 x \right)}}{\sqrt{x} \left(3 \sqrt{x} + 1\right)}\right) \left(16 \log{\left(3 \sqrt{x} + 1 \right)} \sin{\left(2 x \right)} + \frac{9 \sin{\left(2 x \right)}}{x \left(3 \sqrt{x} + 1\right)^{2}} - \frac{24 \cos{\left(2 x \right)}}{\sqrt{x} \left(3 \sqrt{x} + 1\right)} + \frac{3 \sin{\left(2 x \right)}}{x^{\frac{3}{2}} \left(3 \sqrt{x} + 1\right)}\right)}{8} - 8 \log{\left(3 \sqrt{x} + 1 \right)} \cos{\left(2 x \right)} - \frac{27 \cos{\left(2 x \right)}}{2 x \left(3 \sqrt{x} + 1\right)^{2}} + \frac{27 \sin{\left(2 x \right)}}{8 x^{2} \left(3 \sqrt{x} + 1\right)^{2}} - \frac{18 \sin{\left(2 x \right)}}{\sqrt{x} \left(3 \sqrt{x} + 1\right)} - \frac{9 \cos{\left(2 x \right)}}{2 x^{\frac{3}{2}} \left(3 \sqrt{x} + 1\right)} + \frac{27 \sin{\left(2 x \right)}}{4 x^{\frac{3}{2}} \left(3 \sqrt{x} + 1\right)^{3}} + \frac{9 \sin{\left(2 x \right)}}{8 x^{\frac{5}{2}} \left(3 \sqrt{x} + 1\right)}\right)

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Gráfico

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

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Solución