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 v
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Derivada de (x+12)e^(12-x)
- Derivada de u/v
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Derivada de x^(1/10)
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Expresiones idénticas
- y=arctg(cos5x)/√cos5x
- y es igual a arctg( coseno de 5x) dividir por √ coseno de 5x
- y=arctgcos5x/√cos5x
- y=arctg(cos5x) dividir por √cos5x
Derivada de y=arctg(cos5x)/√cos5x
Solución
Ha introducido
[src]
atan(cos(5*x)) -------------- __________ \/ cos(5*x)
$$\frac{\operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\sqrt{\cos{\left(5 x \right)}}}$$
atan(cos(5*x))/sqrt(cos(5*x))
Primera derivada
[src]
5*sin(5*x) 5*atan(cos(5*x))*sin(5*x) - ---------------------------- + ------------------------- / 2 \ __________ 3/2 \1 + cos (5*x)/*\/ cos(5*x) 2*cos (5*x)
$$\frac{5 \sin{\left(5 x \right)} \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{2 \cos^{\frac{3}{2}}{\left(5 x \right)}} - \frac{5 \sin{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \sqrt{\cos{\left(5 x \right)}}}$$
Segunda derivada
[src]
/ / 2 \ / 2 \ \ | __________ | 2*sin (5*x) | | 3*sin (5*x)| | | \/ cos(5*x) *|1 + -------------| |2 + -----------|*atan(cos(5*x))| | | 2 | 2 | 2 | | | \ 1 + cos (5*x)/ sin (5*x) \ cos (5*x) / | 25*|- -------------------------------- - --------------------------- + --------------------------------| | 2 / 2 \ 3/2 __________ | \ 1 + cos (5*x) \1 + cos (5*x)/*cos (5*x) 4*\/ cos(5*x) /
$$25 \left(- \frac{\left(1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}\right) \sqrt{\cos{\left(5 x \right)}}}{\cos^{2}{\left(5 x \right)} + 1} + \frac{\left(\frac{3 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 2\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{4 \sqrt{\cos{\left(5 x \right)}}} - \frac{\sin^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \cos^{\frac{3}{2}}{\left(5 x \right)}}\right)$$
Tercera derivada
[src]
/ 2 2 2 2 \
| 6*cos (5*x) 2*sin (5*x) 8*cos (5*x)*sin (5*x) / 2 \ / 2 \ / 2 \ |
|1 - ------------- + ------------- - --------------------- | 2*sin (5*x) | | 3*sin (5*x)| | 15*sin (5*x)| |
| 2 2 2 3*|1 + -------------| 3*|2 + -----------| |14 + ------------|*atan(cos(5*x))|
| 1 + cos (5*x) 1 + cos (5*x) / 2 \ | 2 | | 2 | | 2 | |
| \1 + cos (5*x)/ \ 1 + cos (5*x)/ \ cos (5*x) / \ cos (5*x) / |
125*|--------------------------------------------------------- - --------------------- - ------------------- + ----------------------------------|*sin(5*x)
| 2 / 2 \ / 2 \ 8*cos(5*x) |
\ 1 + cos (5*x) 2*\1 + cos (5*x)/ 4*\1 + cos (5*x)/ /
-----------------------------------------------------------------------------------------------------------------------------------------------------------
__________
\/ cos(5*x)
$$\frac{125 \left(- \frac{3 \left(1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}\right)}{2 \left(\cos^{2}{\left(5 x \right)} + 1\right)} - \frac{3 \left(\frac{3 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 2\right)}{4 \left(\cos^{2}{\left(5 x \right)} + 1\right)} + \frac{\left(\frac{15 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 14\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{8 \cos{\left(5 x \right)}} + \frac{1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1} - \frac{6 \cos^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1} - \frac{8 \sin^{2}{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right)^{2}}}{\cos^{2}{\left(5 x \right)} + 1}\right) \sin{\left(5 x \right)}}{\sqrt{\cos{\left(5 x \right)}}}$$
Gráfico