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Popular >

derivative of arctan(e^{4x})

Solution

derivative of

arctan (e^{4 x})

Solution

\frac{4 e ^{4 x}}{e ^{8 x} + 1}

Solution steps

\frac{d}{d x} (arctan (e^{4 x}))

Apply the chain rule:

\frac{1}{( e ^{4 x} ) ^{2} + 1} \frac{d}{d x} (e^{4 x})

= \frac{1}{( e ^{4 x} ) ^{2} + 1} \frac{d}{d x} (e^{4 x})

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

= \frac{1}{( e ^{4 x} ) ^{2} + 1} e^{4 x} \cdot 4

Simplify

\frac{1}{( e ^{4 x} ) ^{2} + 1} e^{4 x} \cdot 4 : \frac{4 e ^{4 x}}{e ^{8 x} + 1}

= \frac{4 e ^{4 x}}{e ^{8 x} + 1}

Popular Examples

derivative of-5/(\sqrt[3]{x)}derivative of

derivative of arccos(4x^9)derivative of

arccos (4 x^{9})

derivative of y=(x^3)/(1-x^2)derivative of

y = \frac{x ^{3}}{1 - x ^{2}}

x d x = y d y

limit as x approaches infinity+of 1/(sqrt(x^2+x))

x \to \infty + lim (\frac{1}{x ^{2} + x})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(e^{4x}) ?
The derivative of arctan(e^{4x}) is (4e^{4x})/(e^{8x)+1}
What is the first derivative of arctan(e^{4x}) ?
The first derivative of arctan(e^{4x}) is (4e^{4x})/(e^{8x)+1}