What is the derivative of arccos(e^{6x}) ?

The derivative of arccos(e^{6x}) is -(6e^{6x})/(sqrt(1-e^{12x))}

What is the first derivative of arccos(e^{6x}) ?

The first derivative of arccos(e^{6x}) is -(6e^{6x})/(sqrt(1-e^{12x))}

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\frac{d}{d x} (arccos (e^{6 x}))

- \frac{6 e ^{6 x}}{1 - e ^{12 x}}

Solution steps

\frac{d}{d x} (arccos (e^{6 x}))

Apply the chain rule:

- \frac{1}{1 - ( e ^{6 x} ) ^{2}} \frac{d}{d x} (e^{6 x})

= - \frac{1}{1 - ( e ^{6 x} ) ^{2}} \frac{d}{d x} (e^{6 x})

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

Simplify

- \frac{1}{1 - ( e ^{6 x} ) ^{2}} e^{6 x} \cdot 6 : - \frac{6 e ^{6 x}}{1 - e ^{12 x}}

= - \frac{6 e ^{6 x}}{1 - e ^{12 x}}

What is the derivative of arccos(e^{6x}) ?
The derivative of arccos(e^{6x}) is -(6e^{6x})/(sqrt(1-e^{12x))}
What is the first derivative of arccos(e^{6x}) ?
The first derivative of arccos(e^{6x}) is -(6e^{6x})/(sqrt(1-e^{12x))}