What is the derivative of 2^{arctan(x)} ?

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

What is the first derivative of 2^{arctan(x)} ?

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

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derivative of

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

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

Solution steps

\frac{d}{d x} (2^{a r c t a n (x)})

Apply exponent rule:

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

2^{a r c t a n (x)} = e^{a r c t a n (x) l n (2)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (2)})

Apply the chain rule:

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

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

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

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

Simplify

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

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

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