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Popular >

derivative of arctan(4^x)

Solution

\frac{d}{d x} (arctan (4^{x}))

Solution

\frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 6 ^{x} + 1}

Solution steps

\frac{d}{d x} (arctan (4^{x}))

Apply the chain rule:

\frac{1}{( 4 ^{x} ) ^{2} + 1} \frac{d}{d x} (4^{x})

= \frac{1}{( 4 ^{x} ) ^{2} + 1} \frac{d}{d x} (4^{x})

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

= \frac{1}{( 4 ^{x} ) ^{2} + 1} ln (2) \cdot 2^{2 x + 1}

Simplify

\frac{1}{( 4 ^{x} ) ^{2} + 1} ln (2) \cdot 2^{2 x + 1} : \frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 6 ^{x} + 1}

= \frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 6 ^{x} + 1}

Graph

Popular Examples

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\int \frac{( - 2 cos ( x ) )}{sin ^{2} ( x )} d x

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integral of 1/(sqrt(25x^2-49))

\int \frac{1}{25 x ^{2} - 49} d x

Frequently Asked Questions (FAQ)

What is the derivative of arctan(4^x) ?
The derivative of arctan(4^x) is (ln(2)*2^{2x+1})/(16^x+1)
What is the first derivative of arctan(4^x) ?
The first derivative of arctan(4^x) is (ln(2)*2^{2x+1})/(16^x+1)