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 (π-2x)³
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Derivada de y=e×
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Derivada de y*log(5*y-1)
- Derivada de y=ln((sqrt(x))+(sqrt(x+a)))
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Expresiones idénticas
- x^sqrtctgx
- x en el grado raíz cuadrada de ctgx
- x^√ctgx
- xsqrtctgx
Derivada de x^sqrtctgx
Solución
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
/ / 2 \ \
| | 1 cot (x)| |
________ | ________ |- - - -------|*log(x)|
\/ cot(x) |\/ cot(x) \ 2 2 / |
x *|---------- + ----------------------|
| x ________ |
\ \/ cot(x) /
$$x^{\sqrt{\cot{\left(x \right)}}} \left(\frac{\left(- \frac{\cot^{2}{\left(x \right)}}{2} - \frac{1}{2}\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} + \frac{\sqrt{\cot{\left(x \right)}}}{x}\right)$$
Segunda derivada
[src]
/ 2 \
|/ ________ / 2 \ \ |
|| 2*\/ cot(x) \1 + cot (x)/*log(x)| |
||- ------------ + --------------------| 2 |
________ || x ________ | ________ 2 / 2 \ |
\/ cot(x) |\ \/ cot(x) / \/ cot(x) ________ / 2 \ 1 + cot (x) \1 + cot (x)/ *log(x)|
x *|---------------------------------------- - ---------- + \/ cot(x) *\1 + cot (x)/*log(x) - ------------ - ---------------------|
| 4 2 ________ 3/2 |
\ x x*\/ cot(x) 4*cot (x) /
$$x^{\sqrt{\cot{\left(x \right)}}} \left(\frac{\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} - \frac{2 \sqrt{\cot{\left(x \right)}}}{x}\right)^{2}}{4} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{4 \cot^{\frac{3}{2}}{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \sqrt{\cot{\left(x \right)}} - \frac{\cot^{2}{\left(x \right)} + 1}{x \sqrt{\cot{\left(x \right)}}} - \frac{\sqrt{\cot{\left(x \right)}}}{x^{2}}\right)$$
Tercera derivada
[src]
/ 3 / 2 \ \
| / ________ / 2 \ \ / ________ / 2 \ \ | ________ / 2 \ / 2 \| |
| | 2*\/ cot(x) \1 + cot (x)/*log(x)| | 2*\/ cot(x) \1 + cot (x)/*log(x)| |4*\/ cot(x) \1 + cot (x)/ *log(x) ________ / 2 \ 4*\1 + cot (x)/| |
| |- ------------ + --------------------| 3*|- ------------ + --------------------|*|------------ + --------------------- - 4*\/ cot(x) *\1 + cot (x)/*log(x) + ---------------| 2 2 3 |
________ | | x ________ | ________ | x ________ | | 2 3/2 ________ | / 2 \ ________ / 2 \ / 2 \ / 2 \ / 2 \|
\/ cot(x) | \ \/ cot(x) / 2*\/ cot(x) \ \/ cot(x) / \ x cot (x) x*\/ cot(x) / \1 + cot (x)/ *log(x) 3/2 / 2 \ 3*\/ cot(x) *\1 + cot (x)/ 3*\1 + cot (x)/ 3*\1 + cot (x)/ *log(x) 3*\1 + cot (x)/|
x *|- ---------------------------------------- + ------------ + -------------------------------------------------------------------------------------------------------------------------------------- + --------------------- - 2*cot (x)*\1 + cot (x)/*log(x) + -------------------------- - ---------------- - ----------------------- + ---------------|
| 8 3 8 ________ x 3/2 5/2 2 ________|
\ x 2*\/ cot(x) 4*x*cot (x) 8*cot (x) 2*x *\/ cot(x) /
$$x^{\sqrt{\cot{\left(x \right)}}} \left(- \frac{\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} - \frac{2 \sqrt{\cot{\left(x \right)}}}{x}\right)^{3}}{8} + \frac{3 \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} - \frac{2 \sqrt{\cot{\left(x \right)}}}{x}\right) \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{\cot^{\frac{3}{2}}{\left(x \right)}} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \sqrt{\cot{\left(x \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)}{x \sqrt{\cot{\left(x \right)}}} + \frac{4 \sqrt{\cot{\left(x \right)}}}{x^{2}}\right)}{8} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \log{\left(x \right)}}{8 \cot^{\frac{5}{2}}{\left(x \right)}} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{2 \sqrt{\cot{\left(x \right)}}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot^{\frac{3}{2}}{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{4 x \cot^{\frac{3}{2}}{\left(x \right)}} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \sqrt{\cot{\left(x \right)}}}{x} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)}{2 x^{2} \sqrt{\cot{\left(x \right)}}} + \frac{2 \sqrt{\cot{\left(x \right)}}}{x^{3}}\right)$$
Gráfico