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
-
¿Cómo usar?
- Derivada de:
-
Derivada de x^4/3-x
-
Derivada de x^-4/5
-
Derivada de x=1
-
Derivada de x^2*2^x
- Ecuación diferencial:
- y'
-
Expresiones idénticas
- y'=√tan(x- cinco)cos²(x⁵)
- y signo de prima para el primer (1) orden es igual a √ tangente de (x menos 5) coseno de ²(x⁵)
- y signo de prima para el primer (1) orden es igual a √ tangente de (x menos cinco) coseno de ²(x⁵)
- y'=√tanx-5cos²x⁵
-
Expresiones semejantes
- y'=√tan(x+5)cos²(x⁵)
Derivada de y'=√tan(x-5)cos²(x⁵)
Solución
Ha introducido
[src]
____________ 2/ 5\ \/ tan(x - 5) *cos \x /
$$\cos^{2}{\left(x^{5} \right)} \sqrt{\tan{\left(x - 5 \right)}}$$
sqrt(tan(x - 5))*cos(x^5)^2
Primera derivada
[src]
/ 2 \
2/ 5\ |1 tan (x - 5)|
cos \x /*|- + -----------|
\2 2 / 4 ____________ / 5\ / 5\
-------------------------- - 10*x *\/ tan(x - 5) *cos\x /*sin\x /
____________
\/ tan(x - 5)
$$- 10 x^{4} \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)} \sqrt{\tan{\left(x - 5 \right)}} + \frac{\left(\frac{\tan^{2}{\left(x - 5 \right)}}{2} + \frac{1}{2}\right) \cos^{2}{\left(x^{5} \right)}}{\sqrt{\tan{\left(x - 5 \right)}}}$$
Segunda derivada
[src]
/ / 2 \ \ | 2/ 5\ / 2 \ | _____________ 1 + tan (-5 + x)| | | cos \x /*\1 + tan (-5 + x)/*|- 4*\/ tan(-5 + x) + ----------------| | | | 3/2 | 4 / 2 \ / 5\ / 5\| | 3 _____________ / 5 2/ 5\ / 5\ / 5\ 5 2/ 5\\ \ tan (-5 + x) / 10*x *\1 + tan (-5 + x)/*cos\x /*sin\x /| -|10*x *\/ tan(-5 + x) *\- 5*x *sin \x / + 4*cos\x /*sin\x / + 5*x *cos \x // + -------------------------------------------------------------------- + ----------------------------------------| | 4 _____________ | \ \/ tan(-5 + x) /
$$- (\frac{10 x^{4} \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}}{\sqrt{\tan{\left(x - 5 \right)}}} + 10 x^{3} \left(- 5 x^{5} \sin^{2}{\left(x^{5} \right)} + 5 x^{5} \cos^{2}{\left(x^{5} \right)} + 4 \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}\right) \sqrt{\tan{\left(x - 5 \right)}} + \frac{\left(\frac{\tan^{2}{\left(x - 5 \right)} + 1}{\tan^{\frac{3}{2}}{\left(x - 5 \right)}} - 4 \sqrt{\tan{\left(x - 5 \right)}}\right) \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \cos^{2}{\left(x^{5} \right)}}{4})$$
Tercera derivada
[src]
/ 2\
| / 2 \ / 2 \ | / 2 \
2/ 5\ / 2 \ | 3/2 4*\1 + tan (-5 + x)/ 3*\1 + tan (-5 + x)/ | 4 / 2 \ | _____________ 1 + tan (-5 + x)| / 5\ / 5\
cos \x /*\1 + tan (-5 + x)/*|16*tan (-5 + x) - -------------------- + ---------------------| 15*x *\1 + tan (-5 + x)/*|- 4*\/ tan(-5 + x) + ----------------|*cos\x /*sin\x /
| _____________ 5/2 | 3 / 2 \ / 5 2/ 5\ / 5\ / 5\ 5 2/ 5\\ | 3/2 |
2 _____________ / 5 2/ 5\ / 5\ / 5\ 5 2/ 5\ 10 / 5\ / 5\\ \ \/ tan(-5 + x) tan (-5 + x) / 15*x *\1 + tan (-5 + x)/*\- 5*x *sin \x / + 4*cos\x /*sin\x / + 5*x *cos \x // \ tan (-5 + x) /
40*x *\/ tan(-5 + x) *\- 15*x *cos \x / - 3*cos\x /*sin\x / + 15*x *sin \x / + 25*x *cos\x /*sin\x // + ---------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------
8 _____________ 2
\/ tan(-5 + x)
$$\frac{15 x^{4} \left(\frac{\tan^{2}{\left(x - 5 \right)} + 1}{\tan^{\frac{3}{2}}{\left(x - 5 \right)}} - 4 \sqrt{\tan{\left(x - 5 \right)}}\right) \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}}{2} - \frac{15 x^{3} \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \left(- 5 x^{5} \sin^{2}{\left(x^{5} \right)} + 5 x^{5} \cos^{2}{\left(x^{5} \right)} + 4 \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}\right)}{\sqrt{\tan{\left(x - 5 \right)}}} + 40 x^{2} \left(25 x^{10} \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)} + 15 x^{5} \sin^{2}{\left(x^{5} \right)} - 15 x^{5} \cos^{2}{\left(x^{5} \right)} - 3 \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}\right) \sqrt{\tan{\left(x - 5 \right)}} + \frac{\left(\tan^{2}{\left(x - 5 \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x - 5 \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x - 5 \right)}} - \frac{4 \left(\tan^{2}{\left(x - 5 \right)} + 1\right)}{\sqrt{\tan{\left(x - 5 \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x - 5 \right)}\right) \cos^{2}{\left(x^{5} \right)}}{8}$$
Gráfico