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How to use it?
- Derivative of:
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Derivative of cos(5-3*x)
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Derivative of cos^3(t)
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Derivative of asin(y^2)
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Derivative of (5x^2+2)×(x^2-4)^3
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Identical expressions
- (arctg(x)/x)-ln(one +x^ two)
- (arctg(x) divide by x) minus ln(1 plus x squared )
- (arctg(x) divide by x) minus ln(one plus x to the power of two)
- (arctg(x)/x)-ln(1+x2)
- arctgx/x-ln1+x2
- (arctg(x)/x)-ln(1+x²)
- (arctg(x)/x)-ln(1+x to the power of 2)
- arctgx/x-ln1+x^2
- (arctg(x) divide by x)-ln(1+x^2)
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Similar expressions
- (arctg(x)/x)+ln(1+x^2)
- (arctg(x)/x)-ln(1-x^2)
Derivative of (arctg(x)/x)-ln(1+x^2)
The solution
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atan(x) / 2\ ------- - log\1 + x / x
$$- \log{\left(x^{2} + 1 \right)} + \frac{\operatorname{atan}{\left(x \right)}}{x}$$
atan(x)/x - log(1 + x^2)
The first derivative
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1 atan(x) 2*x ---------- - ------- - ------ / 2\ 2 2 x*\1 + x / x 1 + x
$$- \frac{2 x}{x^{2} + 1} + \frac{1}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}{\left(x \right)}}{x^{2}}$$
The second derivative
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/ 2 \ | 1 1 atan(x) 1 2*x | 2*|- ------ - --------- + ------- - ----------- + ---------| | 2 2 3 2 / 2\ 2| | 1 + x / 2\ x x *\1 + x / / 2\ | \ \1 + x / \1 + x / /
$$2 \left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{1}{x^{2} + 1} - \frac{1}{\left(x^{2} + 1\right)^{2}} - \frac{1}{x^{2} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}{\left(x \right)}}{x^{3}}\right)$$
The third derivative
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/ 3 \ | 8*x 3*atan(x) 2 3 4*x 6*x | 2*|- --------- - --------- + ----------- + ----------- + --------- + ---------| | 3 4 2 3 / 2\ 3 2| | / 2\ x / 2\ x *\1 + x / / 2\ / 2\ | \ \1 + x / x*\1 + x / \1 + x / \1 + x / /
$$2 \left(- \frac{8 x^{3}}{\left(x^{2} + 1\right)^{3}} + \frac{6 x}{\left(x^{2} + 1\right)^{2}} + \frac{4 x}{\left(x^{2} + 1\right)^{3}} + \frac{2}{x \left(x^{2} + 1\right)^{2}} + \frac{3}{x^{3} \left(x^{2} + 1\right)} - \frac{3 \operatorname{atan}{\left(x \right)}}{x^{4}}\right)$$