What is the derivative of y=arccos(e^{3x}) ?

The derivative of y=arccos(e^{3x}) is -(3e^{3x})/(sqrt(1-e^{6x))}

What is the first derivative of y=arccos(e^{3x}) ?

The first derivative of y=arccos(e^{3x}) is -(3e^{3x})/(sqrt(1-e^{6x))}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = arccos (e^{3 x})

- \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}}

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