What is (\partial)/(\partial x)(2(x^2+4)^{-1/2}) ?

The answer to (\partial)/(\partial x)(2(x^2+4)^{-1/2}) is -(2x)/((x^2+4)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(2(x^2+4)^{-1/2})

\frac{\partial}{\partial x} (2 (x^{2} + 4)^{- \frac{1}{2}})

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

Solution steps

\frac{\partial}{\partial x} (2 (x^{2} + 4)^{- \frac{1}{2}})

Take the constant out:

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

= 2 \frac{\partial}{\partial x} ((x^{2} + 4)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x ^{2} + 4 ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (x^{2} + 4)

= - \frac{1}{2 ( x ^{2} + 4 ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (x^{2} + 4)

\frac{\partial}{\partial x} (x^{2} + 4) = 2 x

= 2 (- \frac{1}{2 ( x ^{2} + 4 ) ^{\frac{3}{2}}} \cdot 2 x)

Simplify

2 (- \frac{1}{2 ( x ^{2} + 4 ) ^{\frac{3}{2}}} \cdot 2 x) : - \frac{2 x}{( x ^{2} + 4 ) ^{\frac{3}{2}}}

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

6 e^{- 3 t} - t^{2} + 2 t - 8

x \to 0 + lim (x ln (tan (6 x)))

\int - 3 sin (2 x) d x

\int_{- 5}^{0} 25 - x^{2} d x

\frac{d}{d x} (\frac{4 x ^{2} + 8 x + 8}{x})

What is (\partial)/(\partial x)(2(x^2+4)^{-1/2}) ?
The answer to (\partial)/(\partial x)(2(x^2+4)^{-1/2}) is -(2x)/((x^2+4)^{3/2)}