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^-2
-
Derivada de e
-
Derivada de x^(1/2)
-
Derivada de 3*x^2
-
Expresiones idénticas
- y=x/sqrt(x^ dos cos^2*x)
- y es igual a x dividir por raíz cuadrada de (x al cuadrado coseno de al cuadrado multiplicar por x)
- y es igual a x dividir por raíz cuadrada de (x en el grado dos coseno de al cuadrado multiplicar por x)
- y=x/√(x^2cos^2*x)
- y=x/sqrt(x2cos2*x)
- y=x/sqrtx2cos2*x
- y=x/sqrt(x²cos²*x)
- y=x/sqrt(x en el grado 2cos en el grado 2*x)
- y=x/sqrt(x^2cos^2x)
- y=x/sqrt(x2cos2x)
- y=x/sqrtx2cos2x
- y=x/sqrtx^2cos^2x
- y=x dividir por sqrt(x^2cos^2*x)
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(2*x+1)
- sqrt3
- sqrt(t)-1/sqrt(t)
- sqrt(1-x)*cot(5*x)
- sqrt(3*x+1)*sin(2*x)
Derivada de y=x/sqrt(x^2cos^2*x)
Solución
Ha introducido
[src]
x --------------- ____________ / 2 2 \/ x *cos (x)
$$\frac{x}{\sqrt{x^{2} \cos^{2}{\left(x \right)}}}$$
x/sqrt(x^2*cos(x)^2)
Primera derivada
[src]
2 2
1 x*cos (x) - x *cos(x)*sin(x)
--------------- - ----------------------------
____________ 2
/ 2 2 x*|x|*|cos(x)|*cos (x)
\/ x *cos (x)
$$\frac{1}{\sqrt{x^{2} \cos^{2}{\left(x \right)}}} - \frac{- x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + x \cos^{2}{\left(x \right)}}{x \cos^{2}{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|}$$
Segunda derivada
[src]
2 2 2 2 2
/ sign(x) sign(cos(x))*sin(x)\ cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x) 2*(-cos(x) + x*sin(x))*sin(x)
(-cos(x) + x*sin(x))*|- ----------- + -------------------| - ----------------------------------------------------- + -----------------------------
| 2 2 | x*|x|*|cos(x)|*cos(x) |x|*|cos(x)|*cos(x)
\ x *|cos(x)| |x|*cos (x) /
--------------------------------------------------------------------------------------------------------------------------------------------------
cos(x)
$$\frac{\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|}}{\cos{\left(x \right)}}$$
Tercera derivada
[src]
/ 2 2 2 2 2 \
| / sign(x) sign(cos(x))*sin(x)\ 2*(-cos(x) + x*sin(x)) cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x) 2*(-cos(x) + x*sin(x))*sin(x)| / sign(x) sign(cos(x))*sin(x)\ / sign(x) sign(cos(x))*sin(x)\ / 2 2 2 2 2 \ / sign(x) sign(cos(x))*sin(x)\
3*|(-cos(x) + x*sin(x))*|- ----------- + -------------------| - ---------------------- - ----------------------------------------------------- + -----------------------------| 2*(-cos(x) + x*sin(x))*|- ----------- + -------------------| |- ----------- + -------------------|*\cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/ 2*(-cos(x) + x*sin(x))*|- ----------- + -------------------|*sin(x)
/ 2 2 \ | | 2 2 | x*|x|*|cos(x)| x*|x|*|cos(x)|*cos(x) |x|*|cos(x)|*cos(x) | | 2 2 | | 2 2 | | 2 2 | / 2 2 2 2 2 \ / 2 2 2 \ 2 / 2 2 2 2 2 \ 2 / 2 2 2 2 2 \ / 2 2 2 2 2 \
| sign(cos(x)) 2*sign(x) 2*DiracDelta(x) 2*sin (x)*sign(cos(x)) 2*sin (x)*DiracDelta(cos(x)) 2*sign(x)*sign(cos(x))*sin(x)| \ \ x *|cos(x)| |x|*cos (x) / / \ x *|cos(x)| |x|*cos (x) / 2*(-cos(x) + x*sin(x)) \ x *|cos(x)| |x|*cos (x) / 2*(-cos(x) + x*sin(x))*sign(x) \ x *|cos(x)| |x|*cos (x) / 6*(-cos(x) + x*sin(x)) \cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/*sign(x) 2*\- 3*x*cos (x) - 3*cos(x)*sin(x) + 3*x*sin (x) + 2*x *cos(x)*sin(x)/ 2*sin (x)*(-cos(x) + x*sin(x))*sign(cos(x)) 4*\cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/ 6*sin (x)*(-cos(x) + x*sin(x)) \cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/*sign(cos(x))*sin(x) 8*(-cos(x) + x*sin(x))*sin(x) 4*\cos (x) + x *sin (x) - x *cos (x) - 4*x*cos(x)*sin(x)/*sin(x) 2*(-cos(x) + x*sin(x))*sign(cos(x))*sin(x) 2*(-cos(x) + x*sin(x))*sign(x)*sin(x)
- (-cos(x) + x*sin(x))*|- ------------ - ----------- + --------------- - ---------------------- + ---------------------------- + -----------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------ + ---------------------- - --------------------------------------------------------------------------------------------- + ------------------------------ + ------------------------------------------------------------------- + ---------------------- + --------------------------------------------------------------- - ---------------------------------------------------------------------- + ------------------------------------------- + --------------------------------------------------------- + ------------------------------ - --------------------------------------------------------------------------- - ----------------------------- - ---------------------------------------------------------------- - ------------------------------------------ - -------------------------------------
| |x|*cos(x) 3 2 3 2 2 2 | x x |x|*|cos(x)| x*cos(x) 3 cos(x) 2 3 x*|x|*|cos(x)|*cos(x) 3 2 2 3 x*|x|*|cos(x)|*cos(x) 2 2 2
\ x *|cos(x)| x *|cos(x)| |x|*cos (x) |x|*cos (x) x *cos (x) / x *|cos(x)| x *|x|*|cos(x)| x *|cos(x)|*cos(x) |x|*cos (x) x *|x|*|cos(x)|*cos(x) |x|*|cos(x)|*cos (x) x*|x|*cos (x) x*|x|*|cos(x)|*cos (x) x*|x|*cos (x) x *|cos(x)|*cos(x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
cos(x)
$$\frac{\frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{2 \sin^{2}{\left(x \right)} \delta\left(\cos{\left(x \right)}\right)}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{2 \sin^{2}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{3}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos{\left(x \right)} \left|{x}\right|} + \frac{2 \sin{\left(x \right)} \operatorname{sign}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{x^{2} \cos^{2}{\left(x \right)}} + \frac{2 \delta\left(x\right)}{x^{2} \left|{\cos{\left(x \right)}}\right|} - \frac{2 \operatorname{sign}{\left(x \right)}}{x^{3} \left|{\cos{\left(x \right)}}\right|}\right) + \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin^{2}{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{3}{\left(x \right)} \left|{x}\right|} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{\left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right)}{x} - \frac{8 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{x \cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{x \cos{\left(x \right)}} - \frac{4 \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}}{x \cos^{2}{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{\left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{x \cos^{3}{\left(x \right)} \left|{x}\right|} + \frac{3 \left(\left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\frac{\sin{\left(x \right)} \operatorname{sign}{\left(\cos{\left(x \right)} \right)}}{\cos^{2}{\left(x \right)} \left|{x}\right|} - \frac{\operatorname{sign}{\left(x \right)}}{x^{2} \left|{\cos{\left(x \right)}}\right|}\right) + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)}}{\cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|}\right)}{x} - \frac{2 \left(2 x^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 3 x \sin^{2}{\left(x \right)} - 3 x \cos^{2}{\left(x \right)} - 3 \sin{\left(x \right)} \cos{\left(x \right)}\right)}{x \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} - \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2} \cos{\left(x \right)} \left|{\cos{\left(x \right)}}\right|} + \frac{6 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right)}{x^{2} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} + \frac{4 \left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}{x^{2} \cos{\left(x \right)} \left|{x}\right| \left|{\cos{\left(x \right)}}\right|} + \frac{2 \left(x \sin{\left(x \right)} - \cos{\left(x \right)}\right) \operatorname{sign}{\left(x \right)}}{x^{3} \left|{\cos{\left(x \right)}}\right|} + \frac{\left(x^{2} \sin^{2}{\left(x \right)} - x^{2} \cos^{2}{\left(x \right)} - 4 x \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \operatorname{sign}{\left(x \right)}}{x^{3} \cos{\left(x \right)} \left|{\cos{\left(x \right)}}\right|}}{\cos{\left(x \right)}}$$