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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of y=4+6x-3x^4
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Derivative of √x+√x+√x
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Derivative of x*e^(-2x)
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Derivative of x+ln(x^2-4)
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Identical expressions
- arctg(x)^(lnx)
- arctg(x) to the power of (lnx)
- arctg(x)(lnx)
- arctgxlnx
- arctgx^lnx
Derivative of arctg(x)^(lnx)
The solution
You have entered
[src]
log(x) atan (x)
$$\operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
d / log(x) \ --\atan (x)/ dx
$$\frac{d}{d x} \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
Detail solution
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Don't know the steps in finding this derivative.
But the derivative is
The answer is:
The first derivative
[src]
log(x) /log(atan(x)) log(x) \
atan (x)*|------------ + ----------------|
| x / 2\ |
\ \1 + x /*atan(x)/
$$\left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
The second derivative
[src]
/ 2 \
log(x) |/log(atan(x)) log(x) \ log(atan(x)) log(x) 2 2*x*log(x) |
atan (x)*||------------ + ----------------| - ------------ - ------------------ + ------------------ - -----------------|
|| x / 2\ | 2 2 / 2\ 2 |
|\ \1 + x /*atan(x)/ x / 2\ 2 x*\1 + x /*atan(x) / 2\ |
\ \1 + x / *atan (x) \1 + x / *atan(x)/
$$\left(- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right)^{2} - \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} + \frac{2}{x \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} - \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{2}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
The third derivative
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/ 3 2 \
log(x) |/log(atan(x)) log(x) \ 6 /log(atan(x)) log(x) \ /log(atan(x)) log(x) 2 2*x*log(x) \ 2*log(atan(x)) 3 3 2*log(x) 2*log(x) 6*x*log(x) 8*x *log(x) |
atan (x)*||------------ + ----------------| - ----------------- - 3*|------------ + ----------------|*|------------ + ------------------ - ------------------ + -----------------| + -------------- - -------------------- - ------------------- - ----------------- + ------------------ + ------------------ + -----------------|
|| x / 2\ | 2 | x / 2\ | | 2 2 / 2\ 2 | 3 2 2 / 2\ 2 3 3 3 |
|\ \1 + x /*atan(x)/ / 2\ \ \1 + x /*atan(x)/ | x / 2\ 2 x*\1 + x /*atan(x) / 2\ | x / 2\ 2 x *\1 + x /*atan(x) / 2\ / 2\ 3 / 2\ 2 / 2\ |
\ \1 + x / *atan(x) \ \1 + x / *atan (x) \1 + x / *atan(x)/ x*\1 + x / *atan (x) \1 + x / *atan(x) \1 + x / *atan (x) \1 + x / *atan (x) \1 + x / *atan(x)/
$$\left(\frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}{\left(x \right)}} + \frac{6 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{2}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\log{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x}\right) \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{2}{x \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{\log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{2}}\right) - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} - \frac{6}{\left(x^{2} + 1\right)^{2} \operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3} \operatorname{atan}^{3}{\left(x \right)}} - \frac{3}{x \left(x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(x \right)}} - \frac{3}{x^{2} \left(x^{2} + 1\right) \operatorname{atan}{\left(x \right)}} + \frac{2 \log{\left(\operatorname{atan}{\left(x \right)} \right)}}{x^{3}}\right) \operatorname{atan}^{\log{\left(x \right)}}{\left(x \right)}$$
The graph