What is the derivative of f(x)=2sin^3(sqrt(x)) ?

The derivative of f(x)=2sin^3(sqrt(x)) is (3sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

What is the first derivative of f(x)=2sin^3(sqrt(x)) ?

The first derivative of f(x)=2sin^3(sqrt(x)) is (3sin^2(sqrt(x))cos(sqrt(x)))/(sqrt(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = 2 sin^{3} (x)

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x)) = \frac{cos ( x )}{2 x}

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

Simplify

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

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

\int \frac{- 4 x ^{5} - x ^{\frac{3}{4}} - 2}{9 x ^{\frac{4}{3}}} d x

\int 2 x (x^{2} + 7)^{8} d x

\int x (x^{3} - 2 x^{2}) d x

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

\int cos^{3} (\frac{x}{7}) d x

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