What is the derivative of x^{arctan(x)} ?

The derivative of x^{arctan(x)} is x^{arctan(x)}((ln(x)}{x^2+1}+\frac{arctan(x))/x)

What is the first derivative of x^{arctan(x)} ?

The first derivative of x^{arctan(x)} is x^{arctan(x)}((ln(x)}{x^2+1}+\frac{arctan(x))/x)

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derivative of

x^{a r c t a n (x)}

x^{a r c t a n (x)} (\frac{ln ( x )}{x ^{2} + 1} + \frac{arctan ( x )}{x})

Solution steps

\frac{d}{d x} (x^{a r c t a n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{a r c t a n (x)} = e^{a r c t a n (x) l n (x)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (x)})

Apply the chain rule:

e^{a r c t a n (x) l n (x)} \frac{d}{d x} (arctan (x) ln (x))

= e^{a r c t a n (x) l n (x)} \frac{d}{d x} (arctan (x) ln (x))

\frac{d}{d x} (arctan (x) ln (x)) = \frac{ln ( x )}{x ^{2} + 1} + \frac{arctan ( x )}{x}

= e^{a r c t a n (x) l n (x)} (\frac{ln ( x )}{x ^{2} + 1} + \frac{arctan ( x )}{x})

e^{a r c t a n (x) l n (x)} = x^{a r c t a n (x)}

= x^{a r c t a n (x)} (\frac{ln ( x )}{x ^{2} + 1} + \frac{arctan ( x )}{x})

(1 + x)^{\frac{1}{2}}

\frac{d}{d t} (a \cdot e^{- 9 t} \cdot cos (3 t + b))

lo g_{10} (x^{2} + 1)

lo g_{10} (x^{2} + y^{2})

3^{x + 2}

What is the derivative of x^{arctan(x)} ?
The derivative of x^{arctan(x)} is x^{arctan(x)}((ln(x)}{x^2+1}+\frac{arctan(x))/x)
What is the first derivative of x^{arctan(x)} ?
The first derivative of x^{arctan(x)} is x^{arctan(x)}((ln(x)}{x^2+1}+\frac{arctan(x))/x)