What is the derivative of f(x)= 2/3 (x^2+1)^{3/2} ?

The derivative of f(x)= 2/3 (x^2+1)^{3/2} is 2x(x^2+1)^{1/2}

What is the first derivative of f(x)= 2/3 (x^2+1)^{3/2} ?

The first derivative of f(x)= 2/3 (x^2+1)^{3/2} is 2x(x^2+1)^{1/2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{2}{3} (x^{2} + 1)^{\frac{3}{2}}

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

Solution steps

\frac{d}{d x} (\frac{2}{3} (x^{2} + 1)^{\frac{3}{2}})

Take the constant out:

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

= \frac{2}{3} \frac{d}{d x} ((x^{2} + 1)^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x^{2} + 1)

= \frac{3 ( x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x^{2} + 1)

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

= \frac{2}{3} \cdot \frac{3 ( x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 2 x

Simplify

\frac{2}{3} \cdot \frac{3 ( x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 2 x : 2 x (x^{2} + 1)^{\frac{1}{2}}

= 2 x (x^{2} + 1)^{\frac{1}{2}}

y^{^{''}} + y = 0, y (\frac{π}{3}) = 0, y^{^{'}} (\frac{π}{3}) = 6

\int \frac{x + 1}{x ^{2}} d x

\int \frac{1}{x ^{2} + 5 x + 6} d x

y = cos (e^{- t^{2}})

\frac{d}{d x} ((x^{2} + 2) (x^{3} + 1))

What is the derivative of f(x)= 2/3 (x^2+1)^{3/2} ?
The derivative of f(x)= 2/3 (x^2+1)^{3/2} is 2x(x^2+1)^{1/2}
What is the first derivative of f(x)= 2/3 (x^2+1)^{3/2} ?
The first derivative of f(x)= 2/3 (x^2+1)^{3/2} is 2x(x^2+1)^{1/2}