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 √2x
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Derivada de 25/x
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Derivada de x*arcsinx
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Derivada de 2*sin(3*x)
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Expresiones idénticas
- y=cos((arcsin^ cuatro)(5x^ tres))
- y es igual a coseno de ((arc seno de en el grado 4)(5x al cubo ))
- y es igual a coseno de ((arc seno de en el grado cuatro)(5x en el grado tres))
- y=cos((arcsin4)(5x3))
- y=cosarcsin45x3
- y=cos((arcsin⁴)(5x³))
- y=cos((arcsin en el grado 4)(5x en el grado 3))
- y=cosarcsin^45x^3
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Expresiones con funciones
- Coseno cos
- cos(x)^(25)
- cos(5-3*x)
- cos(x)^(100)
- cos(x)^sin(x)
- cos(x)*sin(x)^(2)
- arcsin
- arcsin(x)^sqrt(1-x^2)
- arcsin2^x
- arcsin(4x+1)
- arcsin1/x
Derivada de y=cos((arcsin^4)(5x^3))
Solución
Ha introducido
[src]
/ 4 3\ cos\asin (x)*5*x /
$$\cos{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}$$
cos(asin(x)^4*(5*x^3))
Primera derivada
[src]
/ 3 3 \ | 2 4 20*x *asin (x)| / 4 3\ -|15*x *asin (x) + --------------|*sin\asin (x)*5*x / | ________ | | / 2 | \ \/ 1 - x /
$$- \left(\frac{20 x^{3} \operatorname{asin}^{3}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 15 x^{2} \operatorname{asin}^{4}{\left(x \right)}\right) \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}$$
Segunda derivada
[src]
/ / 2 3 \ 2 \
2 | | 2 6*x 2*x *asin(x) 12*x*asin(x)| / 3 4 \ 3 / 4*x \ 4 / 3 4 \|
-5*x*asin (x)*|2*|3*asin (x) - ------- + ------------ + ------------|*sin\5*x *asin (x)/ + 5*x *|3*asin(x) + -----------| *asin (x)*cos\5*x *asin (x)/|
| | 2 3/2 ________ | | ________| |
| | -1 + x / 2\ / 2 | | / 2 | |
\ \ \1 - x / \/ 1 - x / \ \/ 1 - x / /
$$- 5 x \left(5 x^{3} \left(\frac{4 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right)^{2} \cos{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} \operatorname{asin}^{4}{\left(x \right)} + 2 \left(\frac{2 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x^{2}}{x^{2} - 1} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}^{2}{\left(x \right)}\right) \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}\right) \operatorname{asin}^{2}{\left(x \right)}$$
Tercera derivada
[src]
/ / 3 2 5 2 4 3 2 2 \ 3 / 2 3 \ \ | | 3 12*x 54*x *asin(x) 6*x *asin (x) 18*x *asin(x) 20*x *asin (x) 36*x*asin (x)| / 3 4 \ 6 / 4*x \ 8 / 3 4 \ 3 4 / 4*x \ | 2 6*x 2*x *asin(x) 12*x*asin(x)| / 3 4 \| 5*|- 2*|3*asin (x) + ----------- - ------------- + ------------- + ------------- + -------------- + -------------|*sin\5*x *asin (x)/ + 25*x *|3*asin(x) + -----------| *asin (x)*sin\5*x *asin (x)/ - 30*x *asin (x)*|3*asin(x) + -----------|*|3*asin (x) - ------- + ------------ + ------------|*cos\5*x *asin (x)/|*asin(x) | | 3/2 2 5/2 2 3/2 ________ | | ________| | ________| | 2 3/2 ________ | | | | / 2\ -1 + x / 2\ / 2\ / 2\ / 2 | | / 2 | | / 2 | | -1 + x / 2\ / 2 | | \ \ \1 - x / \1 - x / \-1 + x / \1 - x / \/ 1 - x / \ \/ 1 - x / \ \/ 1 - x / \ \1 - x / \/ 1 - x / /
$$5 \left(25 x^{6} \left(\frac{4 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right)^{3} \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} \operatorname{asin}^{8}{\left(x \right)} - 30 x^{3} \left(\frac{4 x}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}{\left(x \right)}\right) \left(\frac{2 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x^{2}}{x^{2} - 1} + \frac{12 x \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}^{2}{\left(x \right)}\right) \cos{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)} \operatorname{asin}^{4}{\left(x \right)} - 2 \left(\frac{6 x^{5} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{18 x^{4} \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{20 x^{3} \operatorname{asin}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{12 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{54 x^{2} \operatorname{asin}{\left(x \right)}}{x^{2} - 1} + \frac{36 x \operatorname{asin}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 3 \operatorname{asin}^{3}{\left(x \right)}\right) \sin{\left(5 x^{3} \operatorname{asin}^{4}{\left(x \right)} \right)}\right) \operatorname{asin}{\left(x \right)}$$