What is the derivative of (81)/(8(3x+2)^{5/2)} ?

The derivative of (81)/(8(3x+2)^{5/2)} is -(1215)/(16(3x+2)^{7/2)}

What is the first derivative of (81)/(8(3x+2)^{5/2)} ?

The first derivative of (81)/(8(3x+2)^{5/2)} is -(1215)/(16(3x+2)^{7/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{81}{8 ( 3 x + 2 ) ^{\frac{5}{2}}}

- \frac{1215}{16 ( 3 x + 2 ) ^{\frac{7}{2}}}

Solution steps

\frac{d}{d x} (\frac{81}{8 ( 3 x + 2 ) ^{\frac{5}{2}}})

Take the constant out:

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

= \frac{81}{8} \frac{d}{d x} (\frac{1}{( 3 x + 2 ) ^{\frac{5}{2}}})

Apply exponent rule:

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

= \frac{81}{8} \frac{d}{d x} ((3 x + 2)^{- \frac{5}{2}})

Apply the chain rule:

- \frac{5}{2 ( 3 x + 2 ) ^{\frac{7}{2}}} \frac{d}{d x} (3 x + 2)

= - \frac{5}{2 ( 3 x + 2 ) ^{\frac{7}{2}}} \frac{d}{d x} (3 x + 2)

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

= \frac{81}{8} (- \frac{5}{2 ( 3 x + 2 ) ^{\frac{7}{2}}} \cdot 3)

Simplify

\frac{81}{8} (- \frac{5}{2 ( 3 x + 2 ) ^{\frac{7}{2}}} \cdot 3) : - \frac{1215}{16 ( 3 x + 2 ) ^{\frac{7}{2}}}

= - \frac{1215}{16 ( 3 x + 2 ) ^{\frac{7}{2}}}

\int 2 x + \frac{4}{x} d x

\frac{\partial}{\partial x} (5 x + 10 y + 10 x y)

4 t \frac{d y}{d t} + 22 y = 0

n = 1 \sum \infty \frac{n}{n}

\frac{d}{d x} (sec (2 x) + tan (2 x))

What is the derivative of (81)/(8(3x+2)^{5/2)} ?
The derivative of (81)/(8(3x+2)^{5/2)} is -(1215)/(16(3x+2)^{7/2)}
What is the first derivative of (81)/(8(3x+2)^{5/2)} ?
The first derivative of (81)/(8(3x+2)^{5/2)} is -(1215)/(16(3x+2)^{7/2)}