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

The derivative of-2/((1+x^{3/2)}) is 3/((1+x)^{5/2)}

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

The first derivative of-2/((1+x^{3/2)}) is 3/((1+x)^{5/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{3}{( 1 + x ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{3}{2 ( 1 + x ) ^{\frac{5}{2}}} \frac{d}{d x} (1 + x)

= - \frac{3}{2 ( 1 + x ) ^{\frac{5}{2}}} \frac{d}{d x} (1 + x)

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

= - 2 (- \frac{3}{2 ( 1 + x ) ^{\frac{5}{2}}} \cdot 1)

Simplify

- 2 (- \frac{3}{2 ( 1 + x ) ^{\frac{5}{2}}} \cdot 1) : \frac{3}{( 1 + x ) ^{\frac{5}{2}}}

= \frac{3}{( 1 + x ) ^{\frac{5}{2}}}

f (x) = \frac{7}{x + 1}, at x = 7

\int cos (x) cos (y) d x

\int \frac{1}{x ^{14}} d x

\int (5 x + 2)^{2} d x

\int_{0}^{1} 2 π x (x - x^{2}) d x

What is the derivative of-2/((1+x^{3/2)}) ?
The derivative of-2/((1+x^{3/2)}) is 3/((1+x)^{5/2)}
What is the first derivative of-2/((1+x^{3/2)}) ?
The first derivative of-2/((1+x^{3/2)}) is 3/((1+x)^{5/2)}