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Popular Calculus >

derivative of arccos(e^{9x})

Solution

derivative of

arccos (e^{9 x})

Solution

- \frac{9 e ^{9 x}}{1 - e ^{18 x}}

Solution steps

\frac{d}{d x} (arccos (e^{9 x}))

Apply the chain rule:

- \frac{1}{1 - ( e ^{9 x} ) ^{2}} \frac{d}{d x} (e^{9 x})

= - \frac{1}{1 - ( e ^{9 x} ) ^{2}} \frac{d}{d x} (e^{9 x})

\frac{d}{d x} (e^{9 x}) = e^{9 x} \cdot 9

= - \frac{1}{1 - ( e ^{9 x} ) ^{2}} e^{9 x} \cdot 9

Simplify

- \frac{1}{1 - ( e ^{9 x} ) ^{2}} e^{9 x} \cdot 9 : - \frac{9 e ^{9 x}}{1 - e ^{18 x}}

= - \frac{9 e ^{9 x}}{1 - e ^{18 x}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arccos(e^{9x}) ?
The derivative of arccos(e^{9x}) is -(9e^{9x})/(sqrt(1-e^{18x))}
What is the first derivative of arccos(e^{9x}) ?
The first derivative of arccos(e^{9x}) is -(9e^{9x})/(sqrt(1-e^{18x))}