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Popular >

derivative of arctan(5^x)

Solution

\frac{d}{d x} (arctan (5^{x}))

Solution

\frac{ln ( 5 ) \cdot 5 ^{x}}{2 5 ^{x} + 1}

Solution steps

\frac{d}{d x} (arctan (5^{x}))

Apply the chain rule:

\frac{1}{( 5 ^{x} ) ^{2} + 1} \frac{d}{d x} (5^{x})

= \frac{1}{( 5 ^{x} ) ^{2} + 1} \frac{d}{d x} (5^{x})

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

= \frac{1}{( 5 ^{x} ) ^{2} + 1} \cdot 5^{x} ln (5)

Simplify

\frac{1}{( 5 ^{x} ) ^{2} + 1} \cdot 5^{x} ln (5) : \frac{ln ( 5 ) \cdot 5 ^{x}}{2 5 ^{x} + 1}

= \frac{ln ( 5 ) \cdot 5 ^{x}}{2 5 ^{x} + 1}

Popular Examples

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\int \frac{1 - x}{x} d x

limit as x approaches 6+of ln(x-6)

x \to 6 + lim (ln (x - 6))

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\int_{0}^{5} \frac{1}{x ^{\frac{19}{18}}} d x

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Frequently Asked Questions (FAQ)

What is the derivative of arctan(5^x) ?
The derivative of arctan(5^x) is (ln(5)*5^x)/(25^x+1)
What is the first derivative of arctan(5^x) ?
The first derivative of arctan(5^x) is (ln(5)*5^x)/(25^x+1)