Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of 3^-x
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Derivative of 6^(x^2-8x+28)
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Derivative of x^3*(x^2-1)^2
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Derivative of (x+2)*(x^2-4*x+5)
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Identical expressions
- arctg[ln(ax+b)]
- arctg[ln(ax plus b)]
- arctg[lnax+b]
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Similar expressions
- arctg[ln(ax-b)]
Derivative of arctg[ln(ax+b)]
The solution
You have entered
[src]
atan(log(a*x + b))
$$\operatorname{atan}{\left(\log{\left(a x + b \right)} \right)}$$
atan(log(a*x + b))
The first derivative
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a ----------------------------- / 2 \ \1 + log (a*x + b)/*(a*x + b)
$$\frac{a}{\left(a x + b\right) \left(\log{\left(a x + b \right)}^{2} + 1\right)}$$
The second derivative
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2 / 2*log(b + a*x) \
-a *|1 + -----------------|
| 2 |
\ 1 + log (b + a*x)/
------------------------------
/ 2 \ 2
\1 + log (b + a*x)/*(b + a*x)
$$- \frac{a^{2} \left(1 + \frac{2 \log{\left(a x + b \right)}}{\log{\left(a x + b \right)}^{2} + 1}\right)}{\left(a x + b\right)^{2} \left(\log{\left(a x + b \right)}^{2} + 1\right)}$$
The third derivative
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/ 2 \
3 | 1 3*log(b + a*x) 4*log (b + a*x) |
2*a *|1 - ----------------- + ----------------- + --------------------|
| 2 2 2|
| 1 + log (b + a*x) 1 + log (b + a*x) / 2 \ |
\ \1 + log (b + a*x)/ /
-----------------------------------------------------------------------
/ 2 \ 3
\1 + log (b + a*x)/*(b + a*x)
$$\frac{2 a^{3} \left(1 + \frac{3 \log{\left(a x + b \right)}}{\log{\left(a x + b \right)}^{2} + 1} - \frac{1}{\log{\left(a x + b \right)}^{2} + 1} + \frac{4 \log{\left(a x + b \right)}^{2}}{\left(\log{\left(a x + b \right)}^{2} + 1\right)^{2}}\right)}{\left(a x + b\right)^{3} \left(\log{\left(a x + b \right)}^{2} + 1\right)}$$