en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sin^3(x/3)

Solution

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

Solution

sin^{2} (\frac{x}{3}) cos (\frac{x}{3})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (\frac{x}{3})) = cos (\frac{x}{3}) \frac{1}{3}

= 3 (sin (\frac{x}{3}))^{2} cos (\frac{x}{3}) \frac{1}{3}

Simplify

3 sin^{2} (\frac{x}{3}) cos (\frac{x}{3}) \frac{1}{3} : sin^{2} (\frac{x}{3}) cos (\frac{x}{3})

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

Popular Examples

integral of (sqrt(x))/(x+2)

\int \frac{x}{x + 2} d x

sum from n=1 to infinity of (n!)/(2n!)

n = 1 \sum \infty \frac{n !}{2 n !}

derivative of 2/(x^5)

\frac{d}{d x} (\frac{2}{x ^{5}})

derivative of f(x)2z(9z^2-3z+1)^4 derivative of

f (x) 2 z (9 z^{2} - 3 z + 1)^{4}

integral from pi/6 to pi of sin(θ)

\int_{\frac{π}{6}}^{π} sin (θ) d θ

Frequently Asked Questions (FAQ)

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