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

The derivative of 3/(8(x+1^{5/2)}) is -(15)/(16(x+1)^{7/2)}

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

The first derivative of 3/(8(x+1^{5/2)}) is -(15)/(16(x+1)^{7/2)}

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

- \frac{15}{16 ( x + 1 ) ^{\frac{7}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{5}{2 ( x + 1 ) ^{\frac{7}{2}}} \frac{d}{d x} (x + 1)

= - \frac{5}{2 ( x + 1 ) ^{\frac{7}{2}}} \frac{d}{d x} (x + 1)

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

= \frac{3}{8} (- \frac{5}{2 ( x + 1 ) ^{\frac{7}{2}}} \cdot 1)

Simplify

\frac{3}{8} (- \frac{5}{2 ( x + 1 ) ^{\frac{7}{2}}} \cdot 1) : - \frac{15}{16 ( x + 1 ) ^{\frac{7}{2}}}

= - \frac{15}{16 ( x + 1 ) ^{\frac{7}{2}}}

(e^{x})^{^{'}}

\int \frac{9}{x ( x ^{4} + 7 )} d x

\int 2 x^{2} cos (x^{3}) d x

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

ln (x^{3} + 3 x^{2} + 5 x + 6)

What is the derivative of 3/(8(x+1^{5/2)}) ?
The derivative of 3/(8(x+1^{5/2)}) is -(15)/(16(x+1)^{7/2)}
What is the first derivative of 3/(8(x+1^{5/2)}) ?
The first derivative of 3/(8(x+1^{5/2)}) is -(15)/(16(x+1)^{7/2)}