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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 f(x)=4x^6+7x^5+1
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Derivative of cot(cos(2))+((sin(6*x)^(2))/cos(12*x))*(1/6)
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Derivative of (2*x+3)^5
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Derivative of x^-tan(x)
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Identical expressions
- x^-tan(x)
- x to the power of minus tangent of (x)
- x-tan(x)
- x-tanx
- x^-tanx
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Similar expressions
- x^+tan(x)
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What you mean?
- x/x^tan(x)
You entered:
x^-tan(x)
What you mean?
Derivative of x^-tan(x)
The solution
You have entered
[src]
-tan(x) x
$$x^{- \tan{\left(x \right)}}$$
d / -tan(x)\ --\x / dx
$$\frac{d}{d x} x^{- \tan{\left(x \right)}}$$
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]
-tan(x) // 2 \ tan(x)\
x *|\-1 - tan (x)/*log(x) - ------|
\ x /
$$x^{- \tan{\left(x \right)}} \left(\left(- \tan^{2}{\left(x \right)} - 1\right) \log{\left(x \right)} - \frac{\tan{\left(x \right)}}{x}\right)$$
The second derivative
[src]
/ 2 / 2 \ \
-tan(x) |/tan(x) / 2 \ \ tan(x) 2*\1 + tan (x)/ / 2 \ |
x *||------ + \1 + tan (x)/*log(x)| + ------ - --------------- - 2*\1 + tan (x)/*log(x)*tan(x)|
|\ x / 2 x |
\ x /
$$x^{- \tan{\left(x \right)}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)$$
The third derivative
[src]
/ 3 2 / 2 \ / / 2 \ \ / 2 \ \
-tan(x) | /tan(x) / 2 \ \ 2*tan(x) / 2 \ 3*\1 + tan (x)/ /tan(x) / 2 \ \ | tan(x) 2*\1 + tan (x)/ / 2 \ | 6*\1 + tan (x)/*tan(x) 2 / 2 \ |
x *|- |------ + \1 + tan (x)/*log(x)| - -------- - 2*\1 + tan (x)/ *log(x) + --------------- + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| - ---------------------- - 4*tan (x)*\1 + tan (x)/*log(x)|
| \ x / 3 2 \ x / | 2 x | x |
\ x x \ x / /
$$x^{- \tan{\left(x \right)}} \left(- \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) - 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}\right)$$
The graph