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Popular >

derivative of arccos(e^{3x})

Solution

derivative of

arccos (e^{3 x})

Solution

- \frac{3 e ^{3 x}}{1 - e ^{6 x}}

Solution steps

\frac{d}{d x} (arccos (e^{3 x}))

Apply the chain rule:

- \frac{1}{1 - ( e ^{3 x} ) ^{2}} \frac{d}{d x} (e^{3 x})

= - \frac{1}{1 - ( e ^{3 x} ) ^{2}} \frac{d}{d x} (e^{3 x})

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= - \frac{1}{1 - ( e ^{3 x} ) ^{2}} e^{3 x} \cdot 3

Simplify

- \frac{1}{1 - ( e ^{3 x} ) ^{2}} e^{3 x} \cdot 3 : - \frac{3 e ^{3 x}}{1 - e ^{6 x}}

= - \frac{3 e ^{3 x}}{1 - e ^{6 x}}

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Frequently Asked Questions (FAQ)

What is the derivative of arccos(e^{3x}) ?
The derivative of arccos(e^{3x}) is -(3e^{3x})/(sqrt(1-e^{6x))}
What is the first derivative of arccos(e^{3x}) ?
The first derivative of arccos(e^{3x}) is -(3e^{3x})/(sqrt(1-e^{6x))}