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How to use it?
- Derivative of:
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Derivative of -e^x
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Derivative of x^5-5*x^3-20*x
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Derivative of -x^5+2*x^3-3*x^2-1
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Derivative of x^4/(x^3-1)
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Identical expressions
- atan(x)*log(two *x+ three)
- arc tangent of gent of (x) multiply by logarithm of (2 multiply by x plus 3)
- arc tangent of gent of (x) multiply by logarithm of (two multiply by x plus three)
- atan(x)log(2x+3)
- atanxlog2x+3
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Similar expressions
- atan(x)*log(2*x-3)
- arctan(x)*log(2*x+3)
- arctanx*log(2*x+3)
Derivative of atan(x)*log(2*x+3)
The solution
You have entered
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atan(x)*log(2*x + 3)
$$\log{\left(2 x + 3 \right)} \operatorname{atan}{\left(x \right)}$$
atan(x)*log(2*x + 3)
The first derivative
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log(2*x + 3) 2*atan(x)
------------ + ---------
2 2*x + 3
1 + x
$$\frac{\log{\left(2 x + 3 \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{2 x + 3}$$
The second derivative
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/ 2*atan(x) 2 x*log(3 + 2*x)\ 2*|- ---------- + ------------------ - --------------| | 2 / 2\ 2 | | (3 + 2*x) \1 + x /*(3 + 2*x) / 2\ | \ \1 + x / /
$$2 \left(- \frac{x \log{\left(2 x + 3 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{\left(2 x + 3\right) \left(x^{2} + 1\right)} - \frac{2 \operatorname{atan}{\left(x \right)}}{\left(2 x + 3\right)^{2}}\right)$$
The third derivative
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/ / 2 \ \ | | 4*x | | | |-1 + ------|*log(3 + 2*x) | | | 2| | | 6 8*atan(x) \ 1 + x / 6*x | 2*|- ------------------- + ---------- + -------------------------- - -------------------| | / 2\ 2 3 2 2 | | \1 + x /*(3 + 2*x) (3 + 2*x) / 2\ / 2\ | \ \1 + x / \1 + x / *(3 + 2*x)/
$$2 \left(- \frac{6 x}{\left(2 x + 3\right) \left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 x + 3 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(2 x + 3\right)^{2} \left(x^{2} + 1\right)} + \frac{8 \operatorname{atan}{\left(x \right)}}{\left(2 x + 3\right)^{3}}\right)$$
The graph