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Popular >

derivative of arctan(2^x)

Solution

\frac{d}{d x} (arctan (2^{x}))

Solution

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

Solution steps

\frac{d}{d x} (arctan (2^{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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