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Derivative of e^2*x
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Derivative of cos(x)^2
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Derivative of x^sin(x)
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Identical expressions
- lim(two -2x)^tg*x
- lim(2 minus 2x) to the power of tg multiply by x
- lim(two minus 2x) to the power of tg multiply by x
- lim(2-2x)tg*x
- lim2-2xtg*x
- lim(2-2x)^tgx
- lim(2-2x)tgx
- lim2-2xtgx
- lim2-2x^tgx
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Similar expressions
- lim(2+2x)^tg*x
Derivative of lim(2-2x)^tg*x
The solution
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[src]
tan(x) (2 - 2*x)
$$\left(2 - 2 x\right)^{\tan{\left(x \right)}}$$
(2 - 2*x)^tan(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]
tan(x) // 2 \ 2*tan(x)\
(2 - 2*x) *|\1 + tan (x)/*log(2 - 2*x) - --------|
\ 2 - 2*x /
$$\left(2 - 2 x\right)^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 - 2 x \right)} - \frac{2 \tan{\left(x \right)}}{2 - 2 x}\right)$$
The second derivative
[src]
/ 2 / 2 \ \
tan(x) |/tan(x) / 2 \ \ tan(x) 2*\1 + tan (x)/ / 2 \ |
(2*(1 - x)) *||------ + \1 + tan (x)/*log(2*(1 - x))| - --------- + --------------- + 2*\1 + tan (x)/*log(2*(1 - x))*tan(x)|
|\-1 + x / 2 -1 + x |
\ (-1 + x) /
$$\left(2 \left(1 - x\right)\right)^{\tan{\left(x \right)}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \left(1 - x\right) \right)} + \frac{\tan{\left(x \right)}}{x - 1}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \left(1 - x\right) \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x - 1} - \frac{\tan{\left(x \right)}}{\left(x - 1\right)^{2}}\right)$$
The third derivative
[src]
/ 3 / 2 \ 2 / / 2 \ \ / 2 \ \
tan(x) |/tan(x) / 2 \ \ 3*\1 + tan (x)/ / 2 \ 2*tan(x) /tan(x) / 2 \ \ | tan(x) 2*\1 + tan (x)/ / 2 \ | 2 / 2 \ 6*\1 + tan (x)/*tan(x)|
(2*(1 - x)) *||------ + \1 + tan (x)/*log(2*(1 - x))| - --------------- + 2*\1 + tan (x)/ *log(2*(1 - x)) + --------- + 3*|------ + \1 + tan (x)/*log(2*(1 - x))|*|- --------- + --------------- + 2*\1 + tan (x)/*log(2*(1 - x))*tan(x)| + 4*tan (x)*\1 + tan (x)/*log(2*(1 - x)) + ----------------------|
|\-1 + x / 2 3 \-1 + x / | 2 -1 + x | -1 + x |
\ (-1 + x) (-1 + x) \ (-1 + x) / /
$$\left(2 \left(1 - x\right)\right)^{\tan{\left(x \right)}} \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \left(1 - x\right) \right)} + \frac{\tan{\left(x \right)}}{x - 1}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \left(1 - x\right) \right)} + \frac{\tan{\left(x \right)}}{x - 1}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \left(1 - x\right) \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x - 1} - \frac{\tan{\left(x \right)}}{\left(x - 1\right)^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \left(1 - x\right) \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \left(1 - x\right) \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x - 1} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x - 1\right)^{2}} + \frac{2 \tan{\left(x \right)}}{\left(x - 1\right)^{3}}\right)$$