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Popular >

derivative of arccos(e^{2x})

Solution

derivative of

arccos (e^{2 x})

Solution

- \frac{2 e ^{2 x}}{1 - e ^{4 x}}

Solution steps

\frac{d}{d x} (arccos (e^{2 x}))

Apply the chain rule:

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

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

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

Simplify

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

= - \frac{2 e ^{2 x}}{1 - e ^{4 x}}

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\int_{0}^{\frac{π}{2}} π cos^{2} (x) d x

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\int \frac{x + 9}{x ^{2} + 4} d x

Frequently Asked Questions (FAQ)

What is the derivative of arccos(e^{2x}) ?
The derivative of arccos(e^{2x}) is -(2e^{2x})/(sqrt(1-e^{4x))}
What is the first derivative of arccos(e^{2x}) ?
The first derivative of arccos(e^{2x}) is -(2e^{2x})/(sqrt(1-e^{4x))}