Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de 1/(x+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
- Derivada de y=ax
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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))
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Expresiones semejantes
- y=((3x+1)/(5x+2))^(arcsin(2x))
- 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
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
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 /
$$\left(\frac{3 x - 1}{5 x + 2}\right)^{\operatorname{asin}{\left(2 x \right)}} \left(\frac{\left(5 x + 2\right) \left(- \frac{5 \left(3 x - 1\right)}{\left(5 x + 2\right)^{2}} + \frac{3}{5 x + 2}\right) \operatorname{asin}{\left(2 x \right)}}{3 x - 1} + \frac{2 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\sqrt{1 - 4 x^{2}}}\right)$$
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 / /
$$\left(\frac{3 x - 1}{5 x + 2}\right)^{\operatorname{asin}{\left(2 x \right)}} \left(\frac{8 x \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{3 x - 1} - \frac{2 \log{\left(\frac{3 x - 1}{5 x + 2} \right)}}{\sqrt{1 - 4 x^{2}}}\right)^{2} + \frac{5 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right) \left(5 x + 2\right)} + \frac{3 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(3 x - 1\right)^{2}} - \frac{4 \left(\frac{5 \left(3 x - 1\right)}{5 x + 2} - 3\right)}{\sqrt{1 - 4 x^{2}} \left(3 x - 1\right)}\right)$$
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)$$
Gráfico