What is the derivative of arctan(8^x) ?

The derivative of arctan(8^x) is (3ln(2)*8^x)/(64^x+1)

What is the first derivative of arctan(8^x) ?

The first derivative of arctan(8^x) is (3ln(2)*8^x)/(64^x+1)

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\frac{d}{d x} (arctan (8^{x}))

\frac{3 ln ( 2 ) \cdot 8 ^{x}}{6 4 ^{x} + 1}

Solution steps

\frac{d}{d x} (arctan (8^{x}))

Apply the chain rule:

\frac{1}{( 8 ^{x} ) ^{2} + 1} \frac{d}{d x} (8^{x})

= \frac{1}{( 8 ^{x} ) ^{2} + 1} \frac{d}{d x} (8^{x})

\frac{d}{d x} (8^{x}) = 3 ln (2) \cdot 8^{x}

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

Simplify

\frac{1}{( 8 ^{x} ) ^{2} + 1} \cdot 3 ln (2) \cdot 8^{x} : \frac{3 ln ( 2 ) \cdot 8 ^{x}}{6 4 ^{x} + 1}

= \frac{3 ln ( 2 ) \cdot 8 ^{x}}{6 4 ^{x} + 1}

\int - 0.006 t^{2} + 0.2 t d t

\frac{\partial}{\partial x} (3 x - y - 1)

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

\int \frac{y}{x ^{2} y ^{2} + 1} d x

9 - x^{2}

What is the derivative of arctan(8^x) ?
The derivative of arctan(8^x) is (3ln(2)*8^x)/(64^x+1)
What is the first derivative of arctan(8^x) ?
The first derivative of arctan(8^x) is (3ln(2)*8^x)/(64^x+1)