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
-
Expresiones idénticas
- y=(arcsin4x)/((cos^ cinco)2x)
- y es igual a (arc seno de 4x) dividir por (( coseno de en el grado 5)2x)
- y es igual a (arc seno de 4x) dividir por (( coseno de en el grado cinco)2x)
- y=(arcsin4x)/((cos5)2x)
- y=arcsin4x/cos52x
- y=(arcsin4x)/((cos⁵)2x)
- y=arcsin4x/cos^52x
- y=(arcsin4x) dividir por ((cos^5)2x)
-
Expresiones con funciones
- Coseno cos
- cos(3x^2+2)
Derivada de y=(arcsin4x)/((cos^5)2x)
Solución
Ha introducido
[src]
asin(4*x) ----------- 5 cos (x)*2*x
$$\frac{\operatorname{asin}{\left(4 x \right)}}{x 2 \cos^{5}{\left(x \right)}}$$
asin(4*x)/(((cos(x)^5*2)*x))
Primera derivada
[src]
1
4*-----------
5 / 5 4 \
2*x*cos (x) \- cos (x)*2 + 10*x*cos (x)*sin(x)/*asin(4*x)
-------------- + ---------------------------------------------
___________ 2 10
/ 2 4*x *cos (x)
\/ 1 - 16*x
$$\frac{4 \frac{1}{2 x \cos^{5}{\left(x \right)}}}{\sqrt{1 - 16 x^{2}}} + \frac{\left(10 x \sin{\left(x \right)} \cos^{4}{\left(x \right)} - 2 \cos^{5}{\left(x \right)}\right) \operatorname{asin}{\left(4 x \right)}}{4 x^{2} \cos^{10}{\left(x \right)}}$$
Segunda derivada
[src]
/ / 2 2 \ \
|/ 1 5*sin(x)\ -cos(x) + 5*x*sin(x) 5*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/ 5*(-cos(x) + 5*x*sin(x))*sin(x)|
||- - + --------|*(-cos(x) + 5*x*sin(x)) - -------------------- + --------------------------------------------- + -------------------------------|*asin(4*x)
32 \\ x cos(x) / x cos(x) cos(x) / 4*(-cos(x) + 5*x*sin(x))
-------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------
3/2 2 ___________
/ 2\ 2*x *cos(x) 2 / 2
\1 - 16*x / x *\/ 1 - 16*x *cos(x)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5
cos (x)
$$\frac{\frac{32}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) + \frac{5 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{5 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\cos{\left(x \right)}} - \frac{5 x \sin{\left(x \right)} - \cos{\left(x \right)}}{x}\right) \operatorname{asin}{\left(4 x \right)}}{2 x^{2} \cos{\left(x \right)}} + \frac{4 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2} \sqrt{1 - 16 x^{2}} \cos{\left(x \right)}}}{\cos^{5}{\left(x \right)}}$$
Tercera derivada
[src]
/ / 1 5*sin(x)\ / 1 5*sin(x)\ / 2 2 \ / 1 5*sin(x)\ \
/ 2 \ | / 2 \ / 3 2 3 2 \ |- - + --------|*(-cos(x) + 5*x*sin(x)) / 2 2 \ 5*|- - + --------|*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/ 2 / 2 2 \ 5*|- - + --------|*(-cos(x) + 5*x*sin(x))*sin(x)|
| 48*x | | | 2 30*sin (x) 10*sin(x)| 3*(-cos(x) + 5*x*sin(x)) 5*\3*cos (x) - 12*sin (x)*cos(x) + 12*x*sin (x) - 13*x*cos (x)*sin(x)/ \ x cos(x) / 15*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/ \ x cos(x) / 55*sin (x)*(-cos(x) + 5*x*sin(x)) 75*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/*sin(x) 20*(-cos(x) + 5*x*sin(x))*sin(x) \ x cos(x) / | / / 2 2 \ \
32*|-1 + ----------| |-5*cos(x) + (-cos(x) + 5*x*sin(x))*|5 + -- + ---------- - ---------| + ------------------------ + ---------------------------------------------------------------------- + 25*x*sin(x) - --------------------------------------- - ---------------------------------------------- + -------------------------------------------------------------- + --------------------------------- + ----------------------------------------------------- - -------------------------------- + ------------------------------------------------|*asin(4*x) |/ 1 5*sin(x)\ -cos(x) + 5*x*sin(x) 5*\x*cos (x) - 4*x*sin (x) + 2*cos(x)*sin(x)/ 5*(-cos(x) + 5*x*sin(x))*sin(x)|
| 2| | | 2 2 x*cos(x)| 2 2 x x*cos(x) cos(x) 2 2 x*cos(x) cos(x) | 6*||- - + --------|*(-cos(x) + 5*x*sin(x)) - -------------------- + --------------------------------------------- + -------------------------------|
\ -1 + 16*x / 96*(-cos(x) + 5*x*sin(x)) \ \ x cos (x) / x cos (x) cos (x) cos (x) / \\ x cos(x) / x cos(x) cos(x) /
- -------------------- + ------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------
3/2 3/2 2*x*cos(x) ___________
/ 2\ / 2\ / 2
\1 - 16*x / \1 - 16*x / *cos(x) x*\/ 1 - 16*x *cos(x)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5
x*cos (x)
$$\frac{\frac{96 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}} \cos{\left(x \right)}} - \frac{32 \left(\frac{48 x^{2}}{16 x^{2} - 1} - 1\right)}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{\left(25 x \sin{\left(x \right)} + \frac{5 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{30 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 5 - \frac{10 \sin{\left(x \right)}}{x \cos{\left(x \right)}} + \frac{2}{x^{2}}\right) + \frac{55 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{5 \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\cos{\left(x \right)}} + \frac{75 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{5 \left(12 x \sin^{3}{\left(x \right)} - 13 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} - 12 \sin^{2}{\left(x \right)} \cos{\left(x \right)} + 3 \cos^{3}{\left(x \right)}\right)}{\cos^{2}{\left(x \right)}} - 5 \cos{\left(x \right)} - \frac{\left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right)}{x} - \frac{20 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos{\left(x \right)}} - \frac{15 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{x \cos{\left(x \right)}} + \frac{3 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2}}\right) \operatorname{asin}{\left(4 x \right)}}{2 x \cos{\left(x \right)}} + \frac{6 \left(\left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x}\right) + \frac{5 \left(5 x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{5 \left(- 4 x \sin^{2}{\left(x \right)} + x \cos^{2}{\left(x \right)} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{\cos{\left(x \right)}} - \frac{5 x \sin{\left(x \right)} - \cos{\left(x \right)}}{x}\right)}{x \sqrt{1 - 16 x^{2}} \cos{\left(x \right)}}}{x \cos^{5}{\left(x \right)}}$$
Gráfico