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Popular >

derivative of arccos(e^{4x})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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y^'=(x^2-y^2)/(xy),y(2)=4

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 4

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x \to 2 lim ((2 x - 1)^{2} - x^{2})

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\int_{0}^{\infty} x e^{- \frac{x}{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of arccos(e^{4x}) ?
The derivative of arccos(e^{4x}) is -(4e^{4x})/(sqrt(1-e^{8x))}
What is the first derivative of arccos(e^{4x}) ?
The first derivative of arccos(e^{4x}) is -(4e^{4x})/(sqrt(1-e^{8x))}