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- Derivative of:
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Derivative of sin(2*x^2+3)
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Derivative of (1+x)/(4-x^2)
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Derivative of -1/(x-1)^2
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Derivative of (1+tan(3*x)^(2))*e^(-x/2)
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Identical expressions
- y=tgsqrtxarcctg3x^ five
- y equally tg square root of xarcctg3x to the power of 5
- y equally tg square root of xarcctg3x to the power of five
- y=tg√xarcctg3x^5
- y=tgsqrtxarcctg3x5
- y=tgsqrtxarcctg3x⁵
Derivative of y=tgsqrtxarcctg3x^5
The solution
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/ ___\ 5 tan\\/ x /*acot (3*x)
$$\tan{\left(\sqrt{x} \right)} \operatorname{acot}^{5}{\left(3 x \right)}$$
d / / ___\ 5 \ --\tan\\/ x /*acot (3*x)/ dx
$$\frac{d}{d x} \tan{\left(\sqrt{x} \right)} \operatorname{acot}^{5}{\left(3 x \right)}$$
The first derivative
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5 / 2/ ___\\ 4 / ___\
acot (3*x)*\1 + tan \\/ x // 15*acot (3*x)*tan\\/ x /
---------------------------- - ------------------------
___ 2
2*\/ x 1 + 9*x
$$- \frac{15 \tan{\left(\sqrt{x} \right)} \operatorname{acot}^{4}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{5}{\left(3 x \right)}}{2 \sqrt{x}}$$
The second derivative
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/ / / ___\\ \
| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
| acot (3*x)*\1 + tan \\/ x //*|- ---- + ------------| |
| / ___\ | 3/2 x | / 2/ ___\\ |
3 |90*(2 + 3*x*acot(3*x))*tan\\/ x / \ x / 15*\1 + tan \\/ x //*acot(3*x)|
acot (3*x)*|--------------------------------- + ---------------------------------------------------- - ------------------------------|
| 2 4 ___ / 2\ |
| / 2\ \/ x *\1 + 9*x / |
\ \1 + 9*x / /
$$\left(\frac{\left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{2}{\left(3 x \right)}}{4} + \frac{90 \cdot \left(3 x \operatorname{acot}{\left(3 x \right)} + 2\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} - \frac{15 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)}\right) \operatorname{acot}^{3}{\left(3 x \right)}$$
The third derivative
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/ / 2 2 \ / / ___\ / 2/ ___\\ 2/ ___\\ / / ___\\ \
| | 2 6 36*x*acot(3*x) 36*x *acot (3*x)| / ___\ 3 / 2/ ___\\ | 3 6*tan\\/ x / 2*\1 + tan \\/ x // 4*tan \\/ x /| 2 / 2/ ___\\ | 1 2*tan\\/ x /| |
| 270*|- acot (3*x) + -------- + -------------- + ----------------|*tan\\/ x / acot (3*x)*\1 + tan \\/ x //*|---- - ------------ + ------------------- + -------------| 45*acot (3*x)*\1 + tan \\/ x //*|- ---- + ------------| |
| | 2 2 2 | | 5/2 2 3/2 3/2 | | 3/2 x | / 2/ ___\\ |
2 | \ 1 + 9*x 1 + 9*x 1 + 9*x / \x x x x / \ x / 135*\1 + tan \\/ x //*(2 + 3*x*acot(3*x))*acot(3*x)|
acot (3*x)*|- ---------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- - ------------------------------------------------------- + ---------------------------------------------------|
| 2 8 / 2\ 2 |
| / 2\ 4*\1 + 9*x / ___ / 2\ |
\ \1 + 9*x / \/ x *\1 + 9*x / /
$$\left(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \left(- \frac{6 \tan{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{4 \tan^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \operatorname{acot}^{3}{\left(3 x \right)}}{8} - \frac{45 \cdot \left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}^{2}{\left(3 x \right)}}{4 \cdot \left(9 x^{2} + 1\right)} - \frac{270 \cdot \left(\frac{36 x^{2} \operatorname{acot}^{2}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{36 x \operatorname{acot}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{acot}^{2}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1}\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} + \frac{135 \cdot \left(3 x \operatorname{acot}{\left(3 x \right)} + 2\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{acot}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)^{2}}\right) \operatorname{acot}^{2}{\left(3 x \right)}$$
The graph