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How to use it?
- Derivative of:
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Derivative of x^12
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Derivative of e^-1
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Derivative of sin^3*x
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Derivative of sen2x
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Identical expressions
- (a*arctg(x))/(a+ln(x))
- (a multiply by arctg(x)) divide by (a plus ln(x))
- (aarctg(x))/(a+ln(x))
- aarctgx/a+lnx
- (a*arctg(x)) divide by (a+ln(x))
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Similar expressions
- (a*arctg(x))/(a-ln(x))
Derivative of (a*arctg(x))/(a+ln(x))
The solution
You have entered
[src]
a*atan(x) ---------- a + log(x)
$$\frac{a \operatorname{atan}{\left(x \right)}}{a + \log{\left(x \right)}}$$
(a*atan(x))/(a + log(x))
The first derivative
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a a*atan(x) --------------------- - --------------- / 2\ 2 \1 + x /*(a + log(x)) x*(a + log(x))
$$\frac{a}{\left(a + \log{\left(x \right)}\right) \left(x^{2} + 1\right)} - \frac{a \operatorname{atan}{\left(x \right)}}{x \left(a + \log{\left(x \right)}\right)^{2}}$$
The second derivative
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/ / 2 \ \
| |1 + ----------|*atan(x)|
| 2*x 2 \ a + log(x)/ |
a*|- --------- - ----------------------- + ------------------------|
| 2 / 2\ 2 |
| / 2\ x*\1 + x /*(a + log(x)) x *(a + log(x)) |
\ \1 + x / /
--------------------------------------------------------------------
a + log(x)
$$\frac{a \left(- \frac{2 x}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x \left(a + \log{\left(x \right)}\right) \left(x^{2} + 1\right)} + \frac{\left(1 + \frac{2}{a + \log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \left(a + \log{\left(x \right)}\right)}\right)}{a + \log{\left(x \right)}}$$
The third derivative
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/ / 2 \ \
| | 4*x | / 3 3 \ |
|2*|-1 + ------| 2*|1 + ---------- + -------------|*atan(x) / 2 \ |
| | 2| | a + log(x) 2| 3*|1 + ----------| |
| \ 1 + x / 6 \ (a + log(x)) / \ a + log(x)/ |
a*|--------------- + ---------------------- - ------------------------------------------ + ------------------------|
| 2 2 3 2 / 2\ |
| / 2\ / 2\ x *(a + log(x)) x *\1 + x /*(a + log(x))|
\ \1 + x / \1 + x / *(a + log(x)) /
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a + log(x)
$$\frac{a \left(\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(a + \log{\left(x \right)}\right) \left(x^{2} + 1\right)^{2}} + \frac{3 \left(1 + \frac{2}{a + \log{\left(x \right)}}\right)}{x^{2} \left(a + \log{\left(x \right)}\right) \left(x^{2} + 1\right)} - \frac{2 \left(1 + \frac{3}{a + \log{\left(x \right)}} + \frac{3}{\left(a + \log{\left(x \right)}\right)^{2}}\right) \operatorname{atan}{\left(x \right)}}{x^{3} \left(a + \log{\left(x \right)}\right)}\right)}{a + \log{\left(x \right)}}$$