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Derivative of:
Derivative of cos(x/3)
Derivative of √x
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Derivative of -x^3+(1/2)*x^2-x+1
Identical expressions
lnarctge^x^ two
lnarctge to the power of x squared
lnarctge to the power of x to the power of two
lnarctgex2
lnarctge^x²
lnarctge to the power of x to the power of 2

The derivative of the function/ lnarctge^x^2

Derivative of lnarctge^x^2

The solution

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              / 2\
              \x /
(log(atan(E)))

$$\log{\left(\operatorname{atan}{\left(e \right)} \right)}^{x^{2}}$$

log(atan(E))^(x^2)

Detail solution

Let $u = x^{2}$ .
$\frac{d}{d u} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{u} = \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{u}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
The result of the chain rule is:

$2 x \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{x^{2}}$

The answer is:

$2 x \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                  / 2\                  
                  \x /                  
2*x*(log(atan(E)))    *log(log(atan(E)))

$$2 x \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{x^{2}}$$

Simplify

The second derivative [src]

                / 2\                                               
                \x / /       2                  \                  
2*(log(atan(E)))    *\1 + 2*x *log(log(atan(E)))/*log(log(atan(E)))

$$2 \left(2 x^{2} \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} + 1\right) \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{x^{2}}$$

Simplify

The third derivative [src]

                  / 2\                                                
                  \x /    2               /       2                  \
4*x*(log(atan(E)))    *log (log(atan(E)))*\3 + 2*x *log(log(atan(E)))/

$$4 x \left(2 x^{2} \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)} + 3\right) \log{\left(\log{\left(\operatorname{atan}{\left(e \right)} \right)} \right)}^{2} \log{\left(\operatorname{atan}{\left(e \right)} \right)}^{x^{2}}$$

Simplify

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Identical expressions

Derivative of lnarctge^x^2

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The solution