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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x^{2} + 1)^{- \frac{1}{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\int \frac{7 x ^{2} + 5 x - 6}{( x ^{2} - 4 ) ( x + 2 )} d x

f (x) = x^{4 x}

x \to 1 lim (- 6 x sin (3 x^{2} + 1))

f (x) = \frac{4 x}{x + 2}

\frac{d}{d x} ((x^{2} + 3)^{4} (2 x^{3} - 5)^{3})

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