What is the derivative of 3^{arctan(x}) ?

The derivative of 3^{arctan(x}) is (ln(3)*3^{arctan(x)})/(x^2+1)

What is the first derivative of 3^{arctan(x}) ?

The first derivative of 3^{arctan(x}) is (ln(3)*3^{arctan(x)})/(x^2+1)

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\frac{d}{d x} (3^{a r c t a n (x)})

\frac{ln ( 3 ) \cdot 3 ^{a r c t a n (x)}}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (3^{a r c t a n (x)})

Apply exponent rule:

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

3^{a r c t a n (x)} = e^{a r c t a n (x) l n (3)}

= \frac{d}{d x} (e^{a r c t a n (x) l n (3)})

Apply the chain rule:

e^{a r c t a n (x) l n (3)} \frac{d}{d x} (arctan (x) ln (3))

= e^{a r c t a n (x) l n (3)} \frac{d}{d x} (arctan (x) ln (3))

\frac{d}{d x} (arctan (x) ln (3)) = \frac{ln ( 3 )}{x ^{2} + 1}

= e^{a r c t a n (x) l n (3)} \frac{ln ( 3 )}{x ^{2} + 1}

Simplify

e^{a r c t a n (x) l n (3)} \frac{ln ( 3 )}{x ^{2} + 1} : \frac{ln ( 3 ) \cdot 3 ^{a r c t a n (x)}}{x ^{2} + 1}

= \frac{ln ( 3 ) \cdot 3 ^{a r c t a n (x)}}{x ^{2} + 1}

\frac{\partial}{\partial x} (x y^{2} - 2 y^{3} + 3 x z)

n = 0 \sum \infty \frac{n !}{n ^{3}}

\frac{d}{d x} ((2 x + 3)^{\frac{1}{2}})

\frac{\partial}{\partial x} (3 x^{2} y)

\frac{d}{d x} (sin (x - 2))

What is the derivative of 3^{arctan(x}) ?
The derivative of 3^{arctan(x}) is (ln(3)*3^{arctan(x)})/(x^2+1)
What is the first derivative of 3^{arctan(x}) ?
The first derivative of 3^{arctan(x}) is (ln(3)*3^{arctan(x)})/(x^2+1)