Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of asin(x)
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Derivative of cos(x^3)
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Derivative of (cos(x))^3
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Derivative of 1/tan(x)
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Identical expressions
- (tan(three *x))^sin(x)
- ( tangent of (3 multiply by x)) to the power of sinus of (x)
- ( tangent of (three multiply by x)) to the power of sinus of (x)
- (tan(3*x))sin(x)
- tan3*xsinx
- (tan(3x))^sin(x)
- (tan(3x))sin(x)
- tan3xsinx
- tan3x^sinx
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Similar expressions
- (tan(3*x))^sinx
Derivative of (tan(3*x))^sin(x)
The solution
You have entered
[src]
sin(x) tan (3*x)
$$\tan^{\sin{\left(x \right)}}{\left(3 x \right)}$$
tan(3*x)^sin(x)
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
/ / 2 \ \
sin(x) | \3 + 3*tan (3*x)/*sin(x)|
tan (3*x)*|cos(x)*log(tan(3*x)) + ------------------------|
\ tan(3*x) /
$$\left(\frac{\left(3 \tan^{2}{\left(3 x \right)} + 3\right) \sin{\left(x \right)}}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)} \cos{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(3 x \right)}$$
The second derivative
[src]
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
sin(x) || 3*\1 + tan (3*x)/*sin(x)| / 2 \ 9*\1 + tan (3*x)/ *sin(x) 6*\1 + tan (3*x)/*cos(x)|
tan (3*x)*||cos(x)*log(tan(3*x)) + ------------------------| - log(tan(3*x))*sin(x) + 18*\1 + tan (3*x)/*sin(x) - ------------------------- + ------------------------|
|\ tan(3*x) / 2 tan(3*x) |
\ tan (3*x) /
$$\left(\left(\frac{3 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)} \cos{\left(x \right)}\right)^{2} - \frac{9 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan^{2}{\left(3 x \right)}} + 18 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(3 x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(3 x \right)}} - \log{\left(\tan{\left(3 x \right)} \right)} \sin{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(3 x \right)}$$
The third derivative
[src]
/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
sin(x) || 3*\1 + tan (3*x)/*sin(x)| | 3*\1 + tan (3*x)/*sin(x)| | / 2 \ 6*\1 + tan (3*x)/*cos(x) 9*\1 + tan (3*x)/ *sin(x)| / 2 \ 108*\1 + tan (3*x)/ *sin(x) 27*\1 + tan (3*x)/ *cos(x) 9*\1 + tan (3*x)/*sin(x) 54*\1 + tan (3*x)/ *sin(x) / 2 \ |
tan (3*x)*||cos(x)*log(tan(3*x)) + ------------------------| - cos(x)*log(tan(3*x)) - 3*|cos(x)*log(tan(3*x)) + ------------------------|*|log(tan(3*x))*sin(x) - 18*\1 + tan (3*x)/*sin(x) - ------------------------ + -------------------------| + 54*\1 + tan (3*x)/*cos(x) - --------------------------- - -------------------------- - ------------------------ + -------------------------- + 108*\1 + tan (3*x)/*sin(x)*tan(3*x)|
|\ tan(3*x) / \ tan(3*x) / | tan(3*x) 2 | tan(3*x) 2 tan(3*x) 3 |
\ \ tan (3*x) / tan (3*x) tan (3*x) /
$$\left(\left(\frac{3 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\frac{3 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)} \cos{\left(x \right)}\right) \left(\frac{9 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan^{2}{\left(3 x \right)}} - 18 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(3 x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)} \sin{\left(x \right)}\right) + \frac{54 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{3} \sin{\left(x \right)}}{\tan^{3}{\left(3 x \right)}} - \frac{108 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan{\left(3 x \right)}} - \frac{27 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(3 x \right)}} + 108 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)} \tan{\left(3 x \right)} - \frac{9 \left(\tan^{2}{\left(3 x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(3 x \right)}} + 54 \left(\tan^{2}{\left(3 x \right)} + 1\right) \cos{\left(x \right)} - \log{\left(\tan{\left(3 x \right)} \right)} \cos{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(3 x \right)}$$