en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin^4(6x^2)

Solution

derivative of

sin^{4} (6 x^{2})

Solution

48 x sin^{3} (6 x^{2}) cos (6 x^{2})

Solution steps

\frac{d}{d x} (sin^{4} (6 x^{2}))

Apply the chain rule:

4 (sin (6 x^{2}))^{3} \frac{d}{d x} (sin (6 x^{2}))

= 4 (sin (6 x^{2}))^{3} \frac{d}{d x} (sin (6 x^{2}))

\frac{d}{d x} (sin (6 x^{2})) = cos (6 x^{2}) \cdot 12 x

= 4 (sin (6 x^{2}))^{3} cos (6 x^{2}) \cdot 12 x

Simplify

= 48 x sin^{3} (6 x^{2}) cos (6 x^{2})

Popular Examples

integral of 11x^{4/7}+8x^{-6/7}

\int 11 x^{\frac{4}{7}} + 8 x^{- \frac{6}{7}} d x

integral of (sec(θ))/(cos(θ)-sec(θ))

\int \frac{sec ( θ )}{cos ( θ ) - sec ( θ )} d θ

(dy)/(dx)=1-y^2

\frac{d y}{d x} = 1 - y^{2}

integral of e^x-1/x+4+5x^3

\int e^{x} - \frac{1}{x} + 4 + 5 x^{3} d x

integral of (v^2)/(sqrt(-v^2+3))

\int \frac{v ^{2}}{- v ^{2} + 3} d v

Frequently Asked Questions (FAQ)

What is the derivative of sin^4(6x^2) ?
The derivative of sin^4(6x^2) is 48xsin^3(6x^2)cos(6x^2)
What is the first derivative of sin^4(6x^2) ?
The first derivative of sin^4(6x^2) is 48xsin^3(6x^2)cos(6x^2)