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Popular >

derivative of arctan(7^x)

Solution

\frac{d}{d x} (arctan (7^{x}))

Solution

\frac{ln ( 7 ) \cdot 7 ^{x}}{4 9 ^{x} + 1}

Solution steps

\frac{d}{d x} (arctan (7^{x}))

Apply the chain rule:

\frac{1}{( 7 ^{x} ) ^{2} + 1} \frac{d}{d x} (7^{x})

= \frac{1}{( 7 ^{x} ) ^{2} + 1} \frac{d}{d x} (7^{x})

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

= \frac{1}{( 7 ^{x} ) ^{2} + 1} \cdot 7^{x} ln (7)

Simplify

\frac{1}{( 7 ^{x} ) ^{2} + 1} \cdot 7^{x} ln (7) : \frac{ln ( 7 ) \cdot 7 ^{x}}{4 9 ^{x} + 1}

= \frac{ln ( 7 ) \cdot 7 ^{x}}{4 9 ^{x} + 1}

Popular Examples

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\int \frac{( e ^{a r c t a n (x)} )}{1 + x ^{2}} d x

limit as x approaches 0 of (5sin(2x))/x

x \to 0 lim (\frac{5 sin ( 2 x )}{x})

laplacetransform te^{5t}laplace transform

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w \to - 2 lim (\frac{w + 2}{w ^{2} - 6 w - 16})

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\int tan (t) d t

Frequently Asked Questions (FAQ)

What is the derivative of arctan(7^x) ?
The derivative of arctan(7^x) is (ln(7)*7^x)/(49^x+1)
What is the first derivative of arctan(7^x) ?
The first derivative of arctan(7^x) is (ln(7)*7^x)/(49^x+1)