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- Derivative of:
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Derivative of x^12
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Derivative of -e^x
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Derivative of e^(2-x)
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Derivative of x^2-4*x
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Identical expressions
- y=tgsqrtxarcctg3(x)^ five
- y equally tg square root of xarcctg3(x) to the power of 5
- y equally tg square root of xarcctg3(x) to the power of five
- y=tg√xarcctg3(x)^5
- y=tgsqrtxarcctg3(x)5
- y=tgsqrtxarcctg3x5
- y=tgsqrtxarcctg3(x)⁵
- y=tgsqrtxarcctg3x^5
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Similar expressions
- y=tgsqrtxarcctg3x^5
Derivative of y=tgsqrtxarcctg3(x)^5
The solution
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/ ___\ 243 tan\\/ x /*acot (x)
$$\tan{\left(\sqrt{x} \right)} \operatorname{acot}^{243}{\left(x \right)}$$
tan(sqrt(x))*acot(x)^243
The first derivative
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243 / 2/ ___\\ 242 / ___\
acot (x)*\1 + tan \\/ x // 243*acot (x)*tan\\/ x /
---------------------------- - -------------------------
___ 2
2*\/ x 1 + x
$$- \frac{243 \tan{\left(\sqrt{x} \right)} \operatorname{acot}^{242}{\left(x \right)}}{x^{2} + 1} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{243}{\left(x \right)}}{2 \sqrt{x}}$$
The second derivative
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/ / / ___\\ \
| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
| acot (x)*\1 + tan \\/ x //*|- ---- + ------------| |
| / ___\ | 3/2 x | / 2/ ___\\ |
241 |486*(121 + x*acot(x))*tan\\/ x / \ x / 243*\1 + tan \\/ x //*acot(x)|
acot (x)*|-------------------------------- + -------------------------------------------------- - -----------------------------|
| 2 4 ___ / 2\ |
| / 2\ \/ x *\1 + x / |
\ \1 + x / /
$$\left(\frac{\left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}{4} + \frac{486 \left(x \operatorname{acot}{\left(x \right)} + 121\right) \tan{\left(\sqrt{x} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{243 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)}\right) \operatorname{acot}^{241}{\left(x \right)}$$
The third derivative
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/ / 2 2 \ / / ___\ / 2/ ___\\ 2/ ___\\ / / ___\\ \
| | 2 29161 4*x *acot (x) 726*x*acot(x)| / ___\ 3 / 2/ ___\\ | 3 6*tan\\/ x / 2*\1 + tan \\/ x // 4*tan \\/ x /| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
| 486*|- acot (x) + ------ + ------------- + -------------|*tan\\/ x / acot (x)*\1 + tan \\/ x //*|---- - ------------ + ------------------- + -------------| 729*acot (x)*\1 + tan \\/ x //*|- ---- + ------------| |
| | 2 2 2 | | 5/2 2 3/2 3/2 | | 3/2 x | / 2/ ___\\ |
240 | \ 1 + x 1 + x 1 + x / \x x x x / \ x / 729*\1 + tan \\/ x //*(121 + x*acot(x))*acot(x)|
acot (x)*|- -------------------------------------------------------------------- + -------------------------------------------------------------------------------------- - ------------------------------------------------------ + -----------------------------------------------|
| 2 8 / 2\ 2 |
| / 2\ 4*\1 + x / ___ / 2\ |
\ \1 + x / \/ x *\1 + x / /
$$\left(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \left(- \frac{6 \tan{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{4 \tan^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \operatorname{acot}^{3}{\left(x \right)}}{8} - \frac{729 \left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}{4 \left(x^{2} + 1\right)} - \frac{486 \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{726 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{29161}{x^{2} + 1}\right) \tan{\left(\sqrt{x} \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{729 \left(x \operatorname{acot}{\left(x \right)} + 121\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}}\right) \operatorname{acot}^{240}{\left(x \right)}$$
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