Mister Exam
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How to use it?
- Derivative of:
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Derivative of 7x
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Derivative of 8*x
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Derivative of 4*e^(2*x)
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Derivative of 2^x+1
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Identical expressions
- x^(-tan(x))*x
- x to the power of ( minus tangent of (x)) multiply by x
- x(-tan(x))*x
- x-tanx*x
- x^(-tan(x))x
- x(-tan(x))x
- x-tanxx
- x^-tanxx
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Similar expressions
- x^(tan(x))*x
Derivative of x^(-tan(x))*x
The solution
You have entered
[src]
-tan(x) x *x
$$x x^{- \tan{\left(x \right)}}$$
d / -tan(x) \ --\x *x/ dx
$$\frac{d}{d x} x x^{- \tan{\left(x \right)}}$$
Detail solution
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Apply the quotient rule, which is:
and .
To find :
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Apply the power rule: goes to
To find :
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Don't know the steps in finding this derivative.
But the derivative is
Now plug in to the quotient rule:
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The answer is:
The first derivative
[src]
-tan(x) -tan(x) // 2 \ tan(x)\
x + x*x *|\-1 - tan (x)/*log(x) - ------|
\ x /
$$x x^{- \tan{\left(x \right)}} \left(\left(- \tan^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} - \frac{\tan{\left(x \right)}}{x}\right) + x^{- \tan{\left(x \right)}}$$
The second derivative
[src]
/ / 2 / 2 \ \ \
-tan(x) | |/tan(x) / 2 \ \ tan(x) 2*\1 + tan (x)/ / 2 \ | 2*tan(x) / 2 \ |
x *|x*||------ + \1 + tan (x)/*log(x)| + ------ - --------------- - 2*\1 + tan (x)/*log(x)*tan(x)| - -------- - 2*\1 + tan (x)/*log(x)|
| |\ x / 2 x | x |
\ \ x / /
$$x^{- \tan{\left(x \right)}} \left(x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right) - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{2 \tan{\left(x \right)}}{x}\right)$$
The third derivative
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/ 2 / 3 / 2 \ / / 2 \ \ 2 / 2 \ \ / 2 \ \
-tan(x) | /tan(x) / 2 \ \ |/tan(x) / 2 \ \ 3*\1 + tan (x)/ /tan(x) / 2 \ \ | tan(x) 2*\1 + tan (x)/ / 2 \ | 2*tan(x) / 2 \ 2 / 2 \ 6*\1 + tan (x)/*tan(x)| 6*\1 + tan (x)/ 3*tan(x) / 2 \ |
x *|3*|------ + \1 + tan (x)/*log(x)| - x*||------ + \1 + tan (x)/*log(x)| - --------------- - 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + -------- + 2*\1 + tan (x)/ *log(x) + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------| - --------------- + -------- - 6*\1 + tan (x)/*log(x)*tan(x)|
| \ x / |\ x / 2 \ x / | 2 x | 3 x | x 2 |
\ \ x \ x / x / x /
$$x^{- \tan{\left(x \right)}} \left(- x \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} - 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}\right) + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} - 6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{3 \tan{\left(x \right)}}{x^{2}}\right)$$
The graph