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)

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

\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}

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)