What is the derivative of-1/(4(x+1^{3/2)}) ?

The derivative of-1/(4(x+1^{3/2)}) is 3/(8(x+1)^{5/2)}

What is the first derivative of-1/(4(x+1^{3/2)}) ?

The first derivative of-1/(4(x+1^{3/2)}) is 3/(8(x+1)^{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{1}{4 ( x + 1 ) ^{\frac{3}{2}}})

\frac{3}{8 ( x + 1 ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - \frac{1}{4} (- \frac{3}{2 ( x + 1 ) ^{\frac{5}{2}}} \cdot 1)

Simplify

- \frac{1}{4} (- \frac{3}{2 ( x + 1 ) ^{\frac{5}{2}}} \cdot 1) : \frac{3}{8 ( x + 1 ) ^{\frac{5}{2}}}

= \frac{3}{8 ( x + 1 ) ^{\frac{5}{2}}}

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

\frac{d}{d x} (\frac{- 5}{x})

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

n = 6 \sum \infty e^{7 - 6 n}

\frac{\partial}{\partial x} ((x - y)^{2})

What is the derivative of-1/(4(x+1^{3/2)}) ?
The derivative of-1/(4(x+1^{3/2)}) is 3/(8(x+1)^{5/2)}
What is the first derivative of-1/(4(x+1^{3/2)}) ?
The first derivative of-1/(4(x+1^{3/2)}) is 3/(8(x+1)^{5/2)}