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Derivada de:
Derivada de 1/(x+3)
Derivada de 4-x²
Derivada de 3^(1/x)
Derivada de 2*x+8/x
Expresiones idénticas
y=((3x- uno)/(5x+ dos))^(arcsin(2x))
y es igual a ((3x menos 1) dividir por (5x más 2)) en el grado (arc seno de (2x))
y es igual a ((3x menos uno) dividir por (5x más dos)) en el grado (arc seno de (2x))
y=((3x-1)/(5x+2))(arcsin(2x))
y=3x-1/5x+2arcsin2x
y=3x-1/5x+2^arcsin2x
y=((3x-1) dividir por (5x+2))^(arcsin(2x))
Expresiones semejantes
y=((3x-1)/(5x-2))^(arcsin(2x))
y=((3x+1)/(5x+2))^(arcsin(2x))

Derivada de la función/ y=((3x-1)/(5x+2))^(arcsin(2x))

Derivada de y=((3x-1)/(5x+2))^(arcsin(2x))

Solución

Ha introducido [src]

         asin(2*x)
/3*x - 1\         
|-------|         
\5*x + 2/

\left(\frac{3 x - 1}{5 x + 2}\right)^{\operatorname{asin}{\left(2 x \right)}}

((3*x - 1)/(5*x + 2))^asin(2*x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                   /                 /   3      5*(3*x - 1)\                    \
                   |     /3*x - 1\   |------- - -----------|*(5*x + 2)*asin(2*x)|
         asin(2*x) |2*log|-------|   |5*x + 2             2|                    |
/3*x - 1\          |     \5*x + 2/   \           (5*x + 2) /                    |
|-------|         *|-------------- + -------------------------------------------|
\5*x + 2/          |   __________                      3*x - 1                  |
                   |  /        2                                                |
                   \\/  1 - 4*x                                                 /

\left(\frac{3 x - 1}{5 x + 2}\right)^{\operatorname{asin}{\left(2 x \right)}} \left(\frac{\left(5 x + 2\right) \left(- \frac{5 \left(3 x - 1\right)}{\left(5 x + 2\right)^{2}} + \frac{3}{5 x + 2}\right) \operatorname{asin}{\left(2 x \right)}}{3 x - 1} + \frac{2 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\sqrt{1 - 4 x^{2}}}\right)

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Segunda derivada [src]

                    /                                                   2                                                                                                                   \
                    |/       /-1 + 3*x\   /     5*(-1 + 3*x)\          \       /     5*(-1 + 3*x)\       /     5*(-1 + 3*x)\                    /-1 + 3*x\     /     5*(-1 + 3*x)\          |
          asin(2*x) ||  2*log|--------|   |-3 + ------------|*asin(2*x)|     4*|-3 + ------------|     3*|-3 + ------------|*asin(2*x)   8*x*log|--------|   5*|-3 + ------------|*asin(2*x)|
/-1 + 3*x\          ||       \2 + 5*x /   \       2 + 5*x   /          |       \       2 + 5*x   /       \       2 + 5*x   /                    \2 + 5*x /     \       2 + 5*x   /          |
|--------|         *||- --------------- + -----------------------------|  - ------------------------ + ------------------------------- + ----------------- + -------------------------------|
\2 + 5*x /          ||      __________               -1 + 3*x          |       __________                                  2                         3/2           (-1 + 3*x)*(2 + 5*x)     |
                    ||     /        2                                  |      /        2                         (-1 + 3*x)                /       2\                                       |
                    \\   \/  1 - 4*x                                   /    \/  1 - 4*x  *(-1 + 3*x)                                       \1 - 4*x /                                       /

\left(\frac{3 x - 1}{5 x + 2}\right)^{\operatorname{asin}{\left(2 x \right)}} \left(\frac{8 x \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{3 x - 1} - \frac{2 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\sqrt{1 - 4 x^{2}}}\right)^{2} + \frac{5 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right) \left(5 x + 2\right)} + \frac{3 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right)^{2}} - \frac{4 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right)}{\sqrt{1 - 4 x^{2}} \left(3 x - 1\right)}\right)

Simplificar

Tercera derivada [src]

                    /                                                     3                                                                                                                                                                                                                                                                                                                                                                                                                          \
                    |  /       /-1 + 3*x\   /     5*(-1 + 3*x)\          \      /       /-1 + 3*x\   /     5*(-1 + 3*x)\          \ /     /     5*(-1 + 3*x)\       /     5*(-1 + 3*x)\                    /-1 + 3*x\     /     5*(-1 + 3*x)\          \        /-1 + 3*x\      /     5*(-1 + 3*x)\                  /     5*(-1 + 3*x)\        2    /-1 + 3*x\      /     5*(-1 + 3*x)\                /     5*(-1 + 3*x)\                  /     5*(-1 + 3*x)\            /     5*(-1 + 3*x)\      |
          asin(2*x) |  |  2*log|--------|   |-3 + ------------|*asin(2*x)|      |  2*log|--------|   |-3 + ------------|*asin(2*x)| |   4*|-3 + ------------|     3*|-3 + ------------|*asin(2*x)   8*x*log|--------|   5*|-3 + ------------|*asin(2*x)|   8*log|--------|   18*|-3 + ------------|*asin(2*x)     18*|-3 + ------------|    96*x *log|--------|   50*|-3 + ------------|*asin(2*x)   30*|-3 + ------------|*asin(2*x)   24*x*|-3 + ------------|         30*|-3 + ------------|      |
/-1 + 3*x\          |  |       \2 + 5*x /   \       2 + 5*x   /          |      |       \2 + 5*x /   \       2 + 5*x   /          | |     \       2 + 5*x   /       \       2 + 5*x   /                    \2 + 5*x /     \       2 + 5*x   /          |        \2 + 5*x /      \       2 + 5*x   /                  \       2 + 5*x   /             \2 + 5*x /      \       2 + 5*x   /                \       2 + 5*x   /                  \       2 + 5*x   /            \       2 + 5*x   /      |
|--------|         *|- |- --------------- + -----------------------------|  - 3*|- --------------- + -----------------------------|*|- ------------------------ + ------------------------------- + ----------------- + -------------------------------| + --------------- - -------------------------------- + ------------------------- + ------------------- - -------------------------------- - -------------------------------- - ------------------------ + ----------------------------------|
\2 + 5*x /          |  |      __________               -1 + 3*x          |      |      __________               -1 + 3*x          | |     __________                                  2                         3/2           (-1 + 3*x)*(2 + 5*x)     |              3/2                        3                 __________                            5/2                               2                        2                             3/2                 __________                     |
                    |  |     /        2                                  |      |     /        2                                  | |    /        2                         (-1 + 3*x)                /       2\                                       |    /       2\                 (-1 + 3*x)                 /        2            2      /       2\              (-1 + 3*x)*(2 + 5*x)               (-1 + 3*x) *(2 + 5*x)         /       2\                   /        2                      |
                    \  \   \/  1 - 4*x                                   /      \   \/  1 - 4*x                                   / \  \/  1 - 4*x  *(-1 + 3*x)                                       \1 - 4*x /                                       /    \1 - 4*x /                                          \/  1 - 4*x  *(-1 + 3*x)       \1 - 4*x /                                                                               \1 - 4*x /   *(-1 + 3*x)   \/  1 - 4*x  *(-1 + 3*x)*(2 + 5*x)/

\left(\frac{3 x - 1}{5 x + 2}\right)^{\operatorname{asin}{\left(2 x \right)}} \left(\frac{96 x^{2} \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} - \frac{24 x \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right)}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}} \left(3 x - 1\right)} - \left(\frac{\left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{3 x - 1} - \frac{2 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\sqrt{1 - 4 x^{2}}}\right)^{3} - 3 \left(\frac{\left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{3 x - 1} - \frac{2 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\sqrt{1 - 4 x^{2}}}\right) \left(\frac{8 x \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{5 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right) \left(5 x + 2\right)} + \frac{3 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right)^{2}} - \frac{4 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right)}{\sqrt{1 - 4 x^{2}} \left(3 x - 1\right)}\right) - \frac{50 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right) \left(5 x + 2\right)^{2}} - \frac{30 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right)^{2} \left(5 x + 2\right)} - \frac{18 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right)^{3}} + \frac{30 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right)}{\sqrt{1 - 4 x^{2}} \left(3 x - 1\right) \left(5 x + 2\right)} + \frac{18 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right)}{\sqrt{1 - 4 x^{2}} \left(3 x - 1\right)^{2}} + \frac{8 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)

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Gráfico

Derivada de y=((3x-1)/(5x+2))^(arcsin(2x))

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Expresiones idénticas

Expresiones semejantes

Derivada de y=((3x-1)/(5x+2))^(arcsin(2x))

Gráfico:

Definida a trozos:

Solución