Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of 1/3*x^3
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Derivative of x^2/(x^2+1)
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Derivative of x*sqrt(3-x)
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Derivative of (x^2+25)/x
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Identical expressions
- (tan(x))^sin(x)
- ( tangent of (x)) to the power of sinus of (x)
- (tan(x))sin(x)
- tanxsinx
- tanx^sinx
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Similar expressions
- (tan(x))^sinx
Derivative of (tan(x))^sin(x)
The solution
You have entered
[src]
sin(x) tan (x)
$$\tan^{\sin{\left(x \right)}}{\left(x \right)}$$
tan(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) | \1 + tan (x)/*sin(x)|
tan (x)*|cos(x)*log(tan(x)) + --------------------|
\ tan(x) /
$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(x \right)}$$
The second derivative
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/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
sin(x) || \1 + tan (x)/*sin(x)| / 2 \ \1 + tan (x)/ *sin(x) 2*\1 + tan (x)/*cos(x)|
tan (x)*||cos(x)*log(tan(x)) + --------------------| - log(tan(x))*sin(x) + 2*\1 + tan (x)/*sin(x) - --------------------- + ----------------------|
|\ tan(x) / 2 tan(x) |
\ tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} - \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(x \right)}$$
The third derivative
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/ 3 / 2 \ 2 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
sin(x) || \1 + tan (x)/*sin(x)| | \1 + tan (x)/*sin(x)| | / 2 \ \1 + tan (x)/ *sin(x) 2*\1 + tan (x)/*cos(x)| / 2 \ 4*\1 + tan (x)/ *sin(x) 3*\1 + tan (x)/ *cos(x) 3*\1 + tan (x)/*sin(x) 2*\1 + tan (x)/ *sin(x) / 2 \ |
tan (x)*||cos(x)*log(tan(x)) + --------------------| - cos(x)*log(tan(x)) - 3*|cos(x)*log(tan(x)) + --------------------|*|log(tan(x))*sin(x) - 2*\1 + tan (x)/*sin(x) + --------------------- - ----------------------| + 6*\1 + tan (x)/*cos(x) - ----------------------- - ----------------------- - ---------------------- + ----------------------- + 4*\1 + tan (x)/*sin(x)*tan(x)|
|\ tan(x) / \ tan(x) / | 2 tan(x) | tan(x) 2 tan(x) 3 |
\ \ tan (x) / tan (x) tan (x) /
$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \sin{\left(x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \sin{\left(x \right)}}{\tan{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\tan^{2}{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(x \right)}} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) \tan^{\sin{\left(x \right)}}{\left(x \right)}$$
The graph