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 x^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=(arcsin(5x))^tg√x
- y es igual a (arc seno de (5x)) en el grado tg√x
- y=(arcsin(5x))tg√x
- y=arcsin5xtg√x
- y=arcsin5x^tg√x
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Expresiones con funciones
- arcsin
- arcsin(x)^sqrt(1-x^2)
- arcsin2^x
Derivada de y=(arcsin(5x))^tg√x
Solución
Ha introducido
[src]
/ ___\
tan\\/ x /
(asin(5*x))
$$\operatorname{asin}^{\tan{\left(\sqrt{x} \right)}}{\left(5 x \right)}$$
asin(5*x)^tan(sqrt(x))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ ___\ // 2/ ___\\ / ___\ \
tan\\/ x / |\1 + tan \\/ x //*log(asin(5*x)) 5*tan\\/ x / |
(asin(5*x)) *|-------------------------------- + ------------------------|
| ___ ___________ |
| 2*\/ x / 2 |
\ \/ 1 - 25*x *asin(5*x)/
$$\left(\frac{5 \tan{\left(\sqrt{x} \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{2 \sqrt{x}}\right) \operatorname{asin}^{\tan{\left(\sqrt{x} \right)}}{\left(5 x \right)}$$
Segunda derivada
[src]
/ 2 \
|// 2/ ___\\ / ___\ \ |
||\1 + tan \\/ x //*log(asin(5*x)) 10*tan\\/ x / | |
||-------------------------------- + ------------------------| |
|| ___ ___________ | |
/ ___\ || \/ x / 2 | / ___\ / 2/ ___\\ / 2/ ___\\ / ___\ / 2/ ___\\ / ___\ |
tan\\/ x / |\ \/ 1 - 25*x *asin(5*x)/ 25*tan\\/ x / \1 + tan \\/ x //*log(asin(5*x)) \1 + tan \\/ x //*log(asin(5*x))*tan\\/ x / 5*\1 + tan \\/ x // 125*x*tan\\/ x / |
(asin(5*x)) *|-------------------------------------------------------------- + ----------------------- - -------------------------------- + ------------------------------------------- + ------------------------------ + ------------------------|
| 4 / 2\ 2 3/2 2*x ___________ 3/2 |
| \-1 + 25*x /*asin (5*x) 4*x ___ / 2 / 2\ |
\ \/ x *\/ 1 - 25*x *asin(5*x) \1 - 25*x / *asin(5*x)/
$$\left(\frac{125 x \tan{\left(\sqrt{x} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{\left(\frac{10 \tan{\left(\sqrt{x} \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{\sqrt{x}}\right)^{2}}{4} + \frac{25 \tan{\left(\sqrt{x} \right)}}{\left(25 x^{2} - 1\right) \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)} \tan{\left(\sqrt{x} \right)}}{2 x} + \frac{5 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{\sqrt{x} \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{4 x^{\frac{3}{2}}}\right) \operatorname{asin}^{\tan{\left(\sqrt{x} \right)}}{\left(5 x \right)}$$
Tercera derivada
[src]
/ 3 \
|// 2/ ___\\ / ___\ \ // 2/ ___\\ / ___\ \ / / 2/ ___\\ / ___\ / 2/ ___\\ / ___\ / 2/ ___\\ / ___\ \ |
||\1 + tan \\/ x //*log(asin(5*x)) 10*tan\\/ x / | |\1 + tan \\/ x //*log(asin(5*x)) 10*tan\\/ x / | | \1 + tan \\/ x //*log(asin(5*x)) 100*tan\\/ x / 2*\1 + tan \\/ x //*log(asin(5*x))*tan\\/ x / 20*\1 + tan \\/ x // 500*x*tan\\/ x / | |
||-------------------------------- + ------------------------| 3*|-------------------------------- + ------------------------|*|- -------------------------------- + ----------------------- + --------------------------------------------- + ------------------------------ + ------------------------| |
|| ___ ___________ | | ___ ___________ | | 3/2 / 2\ 2 x ___________ 3/2 | 2 |
/ ___\ || \/ x / 2 | | \/ x / 2 | | x \-1 + 25*x /*asin (5*x) ___ / 2 / 2\ | / ___\ / ___\ / 2/ ___\\ / 2/ ___\\ 2/ ___\ / 2/ ___\\ / ___\ 2 / ___\ / 2/ ___\\ / 2/ ___\\ / ___\ / 2/ ___\\ ___ / 2/ ___\\ / 2/ ___\\ / ___\|
tan\\/ x / |\ \/ 1 - 25*x *asin(5*x)/ \ \/ 1 - 25*x *asin(5*x)/ \ \/ x *\/ 1 - 25*x *asin(5*x) \1 - 25*x / *asin(5*x)/ 125*tan\\/ x / 250*tan\\/ x / \1 + tan \\/ x // *log(asin(5*x)) 3*\1 + tan \\/ x //*log(asin(5*x)) tan \\/ x /*\1 + tan \\/ x //*log(asin(5*x)) 1875*x*tan\\/ x / 9375*x *tan\\/ x / 15*\1 + tan \\/ x // 3*\1 + tan \\/ x //*log(asin(5*x))*tan\\/ x / 75*\1 + tan \\/ x // 375*\/ x *\1 + tan \\/ x // 15*\1 + tan \\/ x //*tan\\/ x /|
(asin(5*x)) *|-------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------ + ------------------------- + --------------------------------- + ---------------------------------- + -------------------------------------------- - ------------------------ + ------------------------ - ------------------------------- - --------------------------------------------- + ------------------------------- + --------------------------- + -------------------------------|
| 8 8 3/2 3/2 3/2 5/2 3/2 2 5/2 ___________ 2 ___ / 2\ 2 3/2 ___________ |
| / 2\ / 2\ 3 4*x 8*x 2*x / 2\ 2 / 2\ 3/2 / 2 4*x 2*\/ x *\-1 + 25*x /*asin (5*x) / 2\ / 2 |
\ \1 - 25*x / *asin(5*x) \1 - 25*x / *asin (5*x) \-1 + 25*x / *asin (5*x) \1 - 25*x / *asin(5*x) 4*x *\/ 1 - 25*x *asin(5*x) 2*\1 - 25*x / *asin(5*x) 2*x*\/ 1 - 25*x *asin(5*x) /
$$\left(\frac{375 \sqrt{x} \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{2 \left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{9375 x^{2} \tan{\left(\sqrt{x} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{1875 x \tan{\left(\sqrt{x} \right)}}{\left(25 x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{\left(\frac{10 \tan{\left(\sqrt{x} \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} + \frac{3 \left(\frac{10 \tan{\left(\sqrt{x} \right)}}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{\sqrt{x}}\right) \left(\frac{500 x \tan{\left(\sqrt{x} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{100 \tan{\left(\sqrt{x} \right)}}{\left(25 x^{2} - 1\right) \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)} \tan{\left(\sqrt{x} \right)}}{x} + \frac{20 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{\sqrt{x} \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{x^{\frac{3}{2}}}\right)}{8} + \frac{125 \tan{\left(\sqrt{x} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{250 \tan{\left(\sqrt{x} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(5 x \right)}} + \frac{15 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \tan{\left(\sqrt{x} \right)}}{2 x \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{3 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)} \tan{\left(\sqrt{x} \right)}}{4 x^{2}} + \frac{75 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{2 \sqrt{x} \left(25 x^{2} - 1\right) \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)^{2} \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{4 x^{\frac{3}{2}}} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)} \tan^{2}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}}} - \frac{15 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{4 x^{\frac{3}{2}} \sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{3 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \log{\left(\operatorname{asin}{\left(5 x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \operatorname{asin}^{\tan{\left(\sqrt{x} \right)}}{\left(5 x \right)}$$
Gráfico