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)

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

\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}

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)