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derivative of arctan(9^x)

Solution

\frac{d}{d x} (arctan (9^{x}))

Solution

\frac{2 ln ( 3 ) \cdot 9 ^{x}}{8 1 ^{x} + 1}

Solution steps

\frac{d}{d x} (arctan (9^{x}))

Apply the chain rule:

\frac{1}{( 9 ^{x} ) ^{2} + 1} \frac{d}{d x} (9^{x})

= \frac{1}{( 9 ^{x} ) ^{2} + 1} \frac{d}{d x} (9^{x})

\frac{d}{d x} (9^{x}) = 2 ln (3) \cdot 9^{x}

= \frac{1}{( 9 ^{x} ) ^{2} + 1} \cdot 2 ln (3) \cdot 9^{x}

Simplify

\frac{1}{( 9 ^{x} ) ^{2} + 1} \cdot 2 ln (3) \cdot 9^{x} : \frac{2 ln ( 3 ) \cdot 9 ^{x}}{8 1 ^{x} + 1}

= \frac{2 ln ( 3 ) \cdot 9 ^{x}}{8 1 ^{x} + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of arctan(9^x) ?
The derivative of arctan(9^x) is (2ln(3)*9^x)/(81^x+1)
What is the first derivative of arctan(9^x) ?
The first derivative of arctan(9^x) is (2ln(3)*9^x)/(81^x+1)