Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
-
How to use it?
- Derivative of:
-
Derivative of (4x-3)^2
-
Derivative of (x^2+1)^4
-
Derivative of -sin(x)+cos(x)
-
Derivative of e^x/x+1
-
Identical expressions
- y=(tan^ two (x))^(sin4x)
- y equally ( tangent of squared (x)) to the power of ( sinus of 4x)
- y equally ( tangent of to the power of two (x)) to the power of ( sinus of 4x)
- y=(tan2(x))(sin4x)
- y=tan2xsin4x
- y=(tan²(x))^(sin4x)
- y=(tan to the power of 2(x)) to the power of (sin4x)
- y=tan^2x^sin4x
Derivative of y=(tan^2(x))^(sin4x)
The solution
You have entered
[src]
sin(4*x) 2 tan (x)
$$\left(\tan^{2}{\left(x \right)}\right)^{\sin{\left(4 x \right)}}$$
(tan(x)^2)^sin(4*x)
Detail solution
-
Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
/ / 2 \ \
2*sin(4*x) | / 2 \ \2 + 2*tan (x)/*sin(4*x)|
|tan(x)| *|4*cos(4*x)*log\tan (x)/ + ------------------------|
\ tan(x) /
$$\left(\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 4 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left|{\tan{\left(x \right)}}\right|^{2 \sin{\left(4 x \right)}}$$
The second derivative
[src]
/ 2 \
| / / 2 \ \ / / 2 \ \ / 2 \ / 2 \ |
2*sin(4*x) | / 2 \ / 2 \ | / 2 \ \1 + tan (x)/*sin(4*x)| | \1 + tan (x)/*sign(tan(x))*sin(4*x)| \1 + tan (x)/ *sin(4*x) 8*\1 + tan (x)/*cos(4*x)|
2*|tan(x)| *|- 8*log\tan (x)/*sin(4*x) + 2*\1 + tan (x)/*sin(4*x) + 2*|2*cos(4*x)*log\tan (x)/ + ----------------------|*|4*cos(4*x)*log(|tan(x)|) + -----------------------------------| - ----------------------- + ------------------------|
| \ tan(x) / \ |tan(x)| / 2 tan(x) |
\ tan (x) /
$$2 \left(2 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + 4 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \cos{\left(4 x \right)}\right) - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)}}{\tan{\left(x \right)}} - 8 \log{\left(\tan^{2}{\left(x \right)} \right)} \sin{\left(4 x \right)}\right) \left|{\tan{\left(x \right)}}\right|^{2 \sin{\left(4 x \right)}}$$
The third derivative
[src]
/ / 2 2 \ / 2 \ 2 3 2 2 \
|/ / 2 \ \ | / 2 \ 2 / 2 \ / 2 \ / 2 \ | / / 2 \ \ | / 2 \ / 2 \ | / / 2 \ \ / / 2 \ \ / 2 \ / 2 \ / 2 \ / 2 \ |
2*sin(4*x) || / 2 \ \1 + tan (x)/*sin(4*x)| | \1 + tan (x)/ *sign (tan(x))*sin(4*x) 2*\1 + tan (x)/ *DiracDelta(tan(x))*sin(4*x) 8*\1 + tan (x)/*cos(4*x)*sign(tan(x)) 2*\1 + tan (x)/*sign(tan(x))*sin(4*x)*tan(x)| / 2 \ | \1 + tan (x)/*sign(tan(x))*sin(4*x)| | / 2 \ / 2 \ \1 + tan (x)/ *sin(4*x) 8*\1 + tan (x)/*cos(4*x)| | \1 + tan (x)/*sign(tan(x))*sin(4*x)| | / 2 \ \1 + tan (x)/*sin(4*x)| / 2 \ \1 + tan (x)/ *sin(4*x) 24*\1 + tan (x)/*sin(4*x) 6*\1 + tan (x)/ *cos(4*x) 2*\1 + tan (x)/ *sin(4*x) / 2 \ |
4*|tan(x)| *||2*cos(4*x)*log\tan (x)/ + ----------------------|*|-16*log(|tan(x)|)*sin(4*x) - ------------------------------------- + -------------------------------------------- + ------------------------------------- + --------------------------------------------| - 16*cos(4*x)*log\tan (x)/ - 2*|4*cos(4*x)*log(|tan(x)|) + -----------------------------------|*|- 2*\1 + tan (x)/*sin(4*x) + 8*log\tan (x)/*sin(4*x) + ----------------------- - ------------------------| + 2*|4*cos(4*x)*log(|tan(x)|) + -----------------------------------| *|2*cos(4*x)*log\tan (x)/ + ----------------------| + 12*\1 + tan (x)/*cos(4*x) + ----------------------- - ------------------------- - ------------------------- - ------------------------- + 2*\1 + tan (x)/*sin(4*x)*tan(x)|
|\ tan(x) / | 2 |tan(x)| |tan(x)| |tan(x)| | \ |tan(x)| / | 2 tan(x) | \ |tan(x)| / \ tan(x) / 3 tan(x) 2 tan(x) |
\ \ tan (x) / \ tan (x) / tan (x) tan (x) /
$$4 \left(2 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + 4 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \cos{\left(4 x \right)}\right)^{2} + \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 2 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left(\frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)} \delta\left(\tan{\left(x \right)}\right)}{\left|{\tan{\left(x \right)}}\right|} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)} \operatorname{sign}^{2}{\left(\tan{\left(x \right)} \right)}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \tan{\left(x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} - 16 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \sin{\left(4 x \right)}\right) - 2 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \operatorname{sign}{\left(\tan{\left(x \right)} \right)}}{\left|{\tan{\left(x \right)}}\right|} + 4 \log{\left(\left|{\tan{\left(x \right)}}\right| \right)} \cos{\left(4 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} - \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)}}{\tan{\left(x \right)}} + 8 \log{\left(\tan^{2}{\left(x \right)} \right)} \sin{\left(4 x \right)}\right) + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(4 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(4 x \right)}}{\tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(4 x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)} \tan{\left(x \right)} - \frac{24 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(4 x \right)}}{\tan{\left(x \right)}} + 12 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(4 x \right)} - 16 \log{\left(\tan^{2}{\left(x \right)} \right)} \cos{\left(4 x \right)}\right) \left|{\tan{\left(x \right)}}\right|^{2 \sin{\left(4 x \right)}}$$