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:
-
Derivada de 6/x
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Derivada de e^(x/2)
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Derivada de (x-1)/(x+1)
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Derivada de -3/x
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Expresiones idénticas
- y=ctg(√x)³×arcsin²x
- y es igual a ctg(√x)³×arc seno de ²x
- y=ctg√x³×arcsin²x
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Expresiones con funciones
- ctg
- ctg^2(3x)
- ctg(x-2)
- ctg^4x
- ctg(x/3)
- ctg(1/x)
Derivada de y=ctg(√x)³×arcsin²x
Solución
Ha introducido
[src]
3/ ___\ 2 cot \\/ x /*asin (x)
$$\cot^{3}{\left(\sqrt{x} \right)} \operatorname{asin}^{2}{\left(x \right)}$$
cot(sqrt(x))^3*asin(x)^2
Primera derivada
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3/ ___\ 2 2/ ___\ / 2/ ___\\
2*cot \\/ x /*asin(x) 3*asin (x)*cot \\/ x /*\-1 - cot \\/ x //
--------------------- + -----------------------------------------
________ ___
/ 2 2*\/ x
\/ 1 - x
$$\frac{2 \cot^{3}{\left(\sqrt{x} \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{3 \left(- \cot^{2}{\left(\sqrt{x} \right)} - 1\right) \cot^{2}{\left(\sqrt{x} \right)} \operatorname{asin}^{2}{\left(x \right)}}{2 \sqrt{x}}$$
Segunda derivada
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/ / / ___\ 2/ ___\ / 2/ ___\\\ \ | 2 / 2/ ___\\ |cot\\/ x / 2*cot \\/ x / 2*\1 + cot \\/ x //| | | 3*asin (x)*\1 + cot \\/ x //*|---------- + ------------- + -------------------| | | | 3/2 x x | / 2/ ___\\ / ___\| | 2/ ___\ / 1 x*asin(x) \ \ x / 6*\1 + cot \\/ x //*asin(x)*cot\\/ x /| / ___\ |2*cot \\/ x /*|- ------- + -----------| + ------------------------------------------------------------------------------- - --------------------------------------|*cot\\/ x / | | 2 3/2| 4 ________ | | | -1 + x / 2\ | ___ / 2 | \ \ \1 - x / / \/ x *\/ 1 - x /
$$\left(2 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \cot^{2}{\left(\sqrt{x} \right)} + \frac{3 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \left(\frac{2 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right)}{x} + \frac{2 \cot^{2}{\left(\sqrt{x} \right)}}{x} + \frac{\cot{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \operatorname{asin}^{2}{\left(x \right)}}{4} - \frac{6 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot{\left(\sqrt{x} \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{x} \sqrt{1 - x^{2}}}\right) \cot{\left(\sqrt{x} \right)}$$
Tercera derivada
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/ 2 \
| / 2/ ___\\ 2/ ___\ 4/ ___\ 3/ ___\ / 2/ ___\\ / ___\ 2/ ___\ / 2/ ___\\| 2/ ___\ / 2/ ___\\ / 1 x*asin(x) \ / / ___\ 2/ ___\ / 2/ ___\\\
2 / 2/ ___\\ |2*\1 + cot \\/ x // 3*cot \\/ x / 4*cot \\/ x / 6*cot \\/ x / 6*\1 + cot \\/ x //*cot\\/ x / 14*cot \\/ x /*\1 + cot \\/ x //| 9*cot \\/ x /*\1 + cot \\/ x //*|- ------- + -----------| / 2/ ___\\ |cot\\/ x / 2*cot \\/ x / 2*\1 + cot \\/ x //| / ___\
3*asin (x)*\1 + cot \\/ x //*|-------------------- + ------------- + ------------- + ------------- + ------------------------------ + --------------------------------| | 2 3/2| 9*\1 + cot \\/ x //*|---------- + ------------- + -------------------|*asin(x)*cot\\/ x /
/ 2 \ | 3/2 5/2 3/2 2 2 3/2 | | -1 + x / 2\ | | 3/2 x x |
3/ ___\ | asin(x) 3*x 3*x *asin(x)| \ x x x x x x / \ \1 - x / / \ x /
2*cot \\/ x /*|----------- + ---------- + ------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------- + -----------------------------------------------------------------------------------------
| 3/2 2 5/2 | 8 ___ ________
|/ 2\ / 2\ / 2\ | \/ x / 2
\\1 - x / \-1 + x / \1 - x / / 2*\/ 1 - x
$$- \frac{3 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \left(\frac{6 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot{\left(\sqrt{x} \right)}}{x^{2}} + \frac{6 \cot^{3}{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right)^{2}}{x^{\frac{3}{2}}} + \frac{14 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{4 \cot^{4}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3 \cot^{2}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}}}\right) \operatorname{asin}^{2}{\left(x \right)}}{8} + 2 \left(\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \cot^{3}{\left(\sqrt{x} \right)} + \frac{9 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \left(\frac{2 \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right)}{x} + \frac{2 \cot^{2}{\left(\sqrt{x} \right)}}{x} + \frac{\cot{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}\right) \cot{\left(\sqrt{x} \right)} \operatorname{asin}{\left(x \right)}}{2 \sqrt{1 - x^{2}}} - \frac{9 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \left(\cot^{2}{\left(\sqrt{x} \right)} + 1\right) \cot^{2}{\left(\sqrt{x} \right)}}{\sqrt{x}}$$
Gráfico