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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\frac{d}{d 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})

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})

\frac{d y}{d x} + 6 (tan (6 x)) y = 9 cos (6 x)

\frac{d}{d x} (8 x^{2} - x^{3})

\int_{0}^{x} cos (t) d t

\frac{d ^{2} y}{d x ^{2}} = \frac{1}{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)