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- Derivative of:
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Derivative of x^2+3x
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Derivative of x^2-3*x+2
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Derivative of (x-2)^2*(x-4)+5
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Derivative of (x^2-1)*(x^4+2)
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Identical expressions
- two ^cosx×arcctg5x^ three
- 2 to the power of co sinus of e of x×arcctg5x cubed
- two to the power of co sinus of e of x×arcctg5x to the power of three
- 2cosx×arcctg5x3
- 2^cosx×arcctg5x³
- 2 to the power of cosx×arcctg5x to the power of 3
Derivative of 2^cosx×arcctg5x^3
The solution
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[src]
cos(x) 3 2 *acot (5*x)
$$2^{\cos{\left(x \right)}} \operatorname{acot}^{3}{\left(5 x \right)}$$
d / cos(x) 3 \ --\2 *acot (5*x)/ dx
$$\frac{d}{d x} 2^{\cos{\left(x \right)}} \operatorname{acot}^{3}{\left(5 x \right)}$$
The first derivative
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cos(x) 2
15*2 *acot (5*x) cos(x) 3
- --------------------- - 2 *acot (5*x)*log(2)*sin(x)
2
1 + 25*x
$$- 2^{\cos{\left(x \right)}} \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}^{3}{\left(5 x \right)} - \frac{15 \cdot 2^{\cos{\left(x \right)}} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1}$$
The second derivative
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cos(x) /150*(1 + 5*x*acot(5*x)) 2 / 2 \ 30*acot(5*x)*log(2)*sin(x)\
2 *|----------------------- + acot (5*x)*\-cos(x) + sin (x)*log(2)/*log(2) + --------------------------|*acot(5*x)
| 2 2 |
| / 2\ 1 + 25*x |
\ \1 + 25*x / /
$$2^{\cos{\left(x \right)}} \left(\left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}^{2}{\left(5 x \right)} + \frac{30 \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{150 \cdot \left(5 x \operatorname{acot}{\left(5 x \right)} + 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right) \operatorname{acot}{\left(5 x \right)}$$
The third derivative
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/ / 2 2 \ \
| | 1 2 30*x*acot(5*x) 100*x *acot (5*x)| |
| 750*|--------- - acot (5*x) + -------------- + -----------------| |
| | 2 2 2 | 2 / 2 \ |
cos(x) | \1 + 25*x 1 + 25*x 1 + 25*x / 3 / 2 2 \ 45*acot (5*x)*\-cos(x) + sin (x)*log(2)/*log(2) 450*(1 + 5*x*acot(5*x))*acot(5*x)*log(2)*sin(x)|
2 *|- ----------------------------------------------------------------- + acot (5*x)*\1 - log (2)*sin (x) + 3*cos(x)*log(2)/*log(2)*sin(x) - ----------------------------------------------- - -----------------------------------------------|
| 2 2 2 |
| / 2\ 1 + 25*x / 2\ |
\ \1 + 25*x / \1 + 25*x / /
$$2^{\cos{\left(x \right)}} \left(\left(- \log{\left(2 \right)}^{2} \sin^{2}{\left(x \right)} + 3 \log{\left(2 \right)} \cos{\left(x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}^{3}{\left(5 x \right)} - \frac{45 \left(\log{\left(2 \right)} \sin^{2}{\left(x \right)} - \cos{\left(x \right)}\right) \log{\left(2 \right)} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1} - \frac{450 \cdot \left(5 x \operatorname{acot}{\left(5 x \right)} + 1\right) \log{\left(2 \right)} \sin{\left(x \right)} \operatorname{acot}{\left(5 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{750 \cdot \left(\frac{100 x^{2} \operatorname{acot}^{2}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{30 x \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} - \operatorname{acot}^{2}{\left(5 x \right)} + \frac{1}{25 x^{2} + 1}\right)}{\left(25 x^{2} + 1\right)^{2}}\right)$$
The graph