What is the derivative of cos(1/4 x^3) ?

The derivative of cos(1/4 x^3) is -(3x^2sin((x^3)/4))/(4)

What is the first derivative of cos(1/4 x^3) ?

The first derivative of cos(1/4 x^3) is -(3x^2sin((x^3)/4))/(4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (cos (\frac{1}{4} x^{3}))

- \frac{3 x ^{2} sin ( \frac{x ^{3}}{4} )}{4}

Solution steps

\frac{d}{d x} (cos (\frac{1}{4} x^{3}))

Simplify

cos (\frac{1}{4} x^{3}) : cos (\frac{x ^{3}}{4})

= \frac{d}{d x} (cos (\frac{x ^{3}}{4}))

Apply the chain rule:

- sin (\frac{x ^{3}}{4}) \frac{d}{d x} (\frac{x ^{3}}{4})

= - sin (\frac{x ^{3}}{4}) \frac{d}{d x} (\frac{x ^{3}}{4})

\frac{d}{d x} (\frac{x ^{3}}{4}) = \frac{3 x ^{2}}{4}

= - sin (\frac{x ^{3}}{4}) \frac{3 x ^{2}}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 x ^{2} sin ( \frac{x ^{3}}{4} )}{4}

What is the derivative of cos(1/4 x^3) ?
The derivative of cos(1/4 x^3) is -(3x^2sin((x^3)/4))/(4)
What is the first derivative of cos(1/4 x^3) ?
The first derivative of cos(1/4 x^3) is -(3x^2sin((x^3)/4))/(4)