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- Derivative of:
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Identical expressions
- e^(tgx)*arcctg^2x
- e to the power of (tgx) multiply by arcctg squared x
- e(tgx)*arcctg2x
- etgx*arcctg2x
- e^(tgx)*arcctg²x
- e to the power of (tgx)*arcctg to the power of 2x
- e^(tgx)arcctg^2x
- e(tgx)arcctg2x
- etgxarcctg2x
- e^tgxarcctg^2x
Derivative of e^(tgx)*arcctg^2x
The solution
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tan(x) 2 E *acot (x)
$$e^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)}$$
E^tan(x)*acot(x)^2
The first derivative
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tan(x)
2 / 2 \ tan(x) 2*acot(x)*e
acot (x)*\1 + tan (x)/*e - -----------------
2
1 + x
$$\left(\tan^{2}{\left(x \right)} + 1\right) e^{\tan{\left(x \right)}} \operatorname{acot}^{2}{\left(x \right)} - \frac{2 e^{\tan{\left(x \right)}} \operatorname{acot}{\left(x \right)}}{x^{2} + 1}$$
The second derivative
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/ / 2 \ \ |2*(1 + 2*x*acot(x)) 2 / 2 \ / 2 \ 4*\1 + tan (x)/*acot(x)| tan(x) |------------------- + acot (x)*\1 + tan (x)/*\1 + tan (x) + 2*tan(x)/ - -----------------------|*e | 2 2 | | / 2\ 1 + x | \ \1 + x / /
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 2 \tan{\left(x \right)} + 1\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}}\right) e^{\tan{\left(x \right)}}$$
The third derivative
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/ / 2 \ \ | | 3*x 4*x *acot(x)| | | 4*|-acot(x) + ------ + ------------| | | | 2 2 | / 2 \ / 2 \ / 2 \ / 2 \ | | \ 1 + x 1 + x / 2 / 2 \ | / 2 \ 2 / 2 \ | 6*\1 + tan (x)/*(1 + 2*x*acot(x)) 6*\1 + tan (x)/*\1 + tan (x) + 2*tan(x)/*acot(x)| tan(x) |- ------------------------------------ + acot (x)*\1 + tan (x)/*\2 + \1 + tan (x)/ + 6*tan (x) + 6*\1 + tan (x)/*tan(x)/ + --------------------------------- - ------------------------------------------------|*e | 2 2 2 | | / 2\ / 2\ 1 + x | \ \1 + x / \1 + x / /
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 6 \tan^{2}{\left(x \right)} + 2\right) \operatorname{acot}^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 2 \tan{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{6 \left(2 x \operatorname{acot}{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}\right) e^{\tan{\left(x \right)}}$$