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/(sqrt(5^2+y^2))
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Derivada de y=(3x-7)4
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Expresiones idénticas
- y=ln(cosx/sqrt(x^ dos))
- y es igual a ln( coseno de x dividir por raíz cuadrada de (x al cuadrado ))
- y es igual a ln( coseno de x dividir por raíz cuadrada de (x en el grado dos))
- y=ln(cosx/√(x^2))
- y=ln(cosx/sqrt(x2))
- y=lncosx/sqrtx2
- y=ln(cosx/sqrt(x²))
- y=ln(cosx/sqrt(x en el grado 2))
- y=lncosx/sqrtx^2
- y=ln(cosx dividir por sqrt(x^2))
Derivada de y=ln(cosx/sqrt(x^2))
Solución
Ha introducido
[src]
/ cos(x)\ log|-------| | ____| | / 2 | \\/ x /
$$\log{\left(\frac{\cos{\left(x \right)}}{\sqrt{x^{2}}} \right)}$$
log(cos(x)/sqrt(x^2))
Primera derivada
[src]
/ sin(x) cos(x)\
|- ------ - ------|*|x|
\ |x| x*|x| /
-----------------------
cos(x)
$$\frac{\left(- \frac{\sin{\left(x \right)}}{\left|{x}\right|} - \frac{\cos{\left(x \right)}}{x \left|{x}\right|}\right) \left|{x}\right|}{\cos{\left(x \right)}}$$
Segunda derivada
[src]
/cos(x) \ /cos(x) \
|------ + sin(x)|*sign(x) |------ + sin(x)|*sin(x)
/ cos(x) sin(x) cos(x)*sign(x) cos(x) sign(x)*sin(x)\ \ x / \ x /
|- ------ + ------ + -------------- + ------ + --------------|*|x| - ------------------------- - ------------------------
| |x| x*|x| 3 2 2 | |x| cos(x)
\ x x *|x| x /
-------------------------------------------------------------------------------------------------------------------------
cos(x)
$$\frac{- \frac{\left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \operatorname{sign}{\left(x \right)}}{\left|{x}\right|} + \left(- \frac{\cos{\left(x \right)}}{\left|{x}\right|} + \frac{\sin{\left(x \right)}}{x \left|{x}\right|} + \frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}}\right) \left|{x}\right|}{\cos{\left(x \right)}}$$
Tercera derivada
[src]
/ cos(x) sin(x) cos(x)*sign(x) cos(x) sign(x)*sin(x)\
/cos(x) \ 2 /cos(x) \ 2*|- ------ + ------ + -------------- + ------ + --------------|*|x|*sin(x) /cos(x) \
2*|------ + sin(x)|*DiracDelta(x) 2*sin (x)*|------ + sin(x)| | |x| x*|x| 3 2 2 | 2*|------ + sin(x)|*sign(x)*sin(x)
/sin(x) cos(x) 4*cos(x)*sign(x) 4*sign(x)*sin(x) 2*cos(x) 2*sin(x) 2*DiracDelta(x)*cos(x) 2*DiracDelta(x)*sin(x) 2*cos(x)*sign(x)\ cos(x) / cos(x) sin(x) cos(x)*sign(x) cos(x) sign(x)*sin(x)\ \ x / \ x / \ x x *|x| x / \ x /
-sin(x) + |------ + ------ - ---------------- - ---------------- - -------- - -------- + ---------------------- + ---------------------- + ----------------|*|x| - ------ + 2*|- ------ + ------ + -------------- + ------ + --------------|*sign(x) - --------------------------------- - --------------------------- + --------------------------------------------------------------------------- - ----------------------------------
| |x| x*|x| 4 3 3 2 3 2 2 | x | |x| x*|x| 3 2 2 | |x| 2 cos(x) |x|*cos(x)
\ x x x *|x| x *|x| x x x / \ x x *|x| x / cos (x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
cos(x)
$$\frac{- \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{\cos{\left(x \right)} \left|{x}\right|} - \frac{2 \left(\sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{x}\right) \delta\left(x\right)}{\left|{x}\right|} + \frac{2 \left(- \frac{\cos{\left(x \right)}}{\left|{x}\right|} + \frac{\sin{\left(x \right)}}{x \left|{x}\right|} + \frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}}\right) \sin{\left(x \right)} \left|{x}\right|}{\cos{\left(x \right)}} + 2 \left(- \frac{\cos{\left(x \right)}}{\left|{x}\right|} + \frac{\sin{\left(x \right)}}{x \left|{x}\right|} + \frac{\sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} + \frac{\cos{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{\cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}}\right) \operatorname{sign}{\left(x \right)} + \left(\frac{\sin{\left(x \right)}}{\left|{x}\right|} + \frac{\cos{\left(x \right)}}{x \left|{x}\right|} + \frac{2 \sin{\left(x \right)} \delta\left(x\right)}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{2} \left|{x}\right|} + \frac{2 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{2}} - \frac{4 \sin{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{3}} + \frac{2 \cos{\left(x \right)} \delta\left(x\right)}{x^{3}} - \frac{2 \cos{\left(x \right)}}{x^{3} \left|{x}\right|} - \frac{4 \cos{\left(x \right)} \operatorname{sign}{\left(x \right)}}{x^{4}}\right) \left|{x}\right| - \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}}{\cos{\left(x \right)}}$$