What is the derivative of 9/(4(3x+2)^{3/2)} ?

The derivative of 9/(4(3x+2)^{3/2)} is -(81)/(8(3x+2)^{5/2)}

What is the first derivative of 9/(4(3x+2)^{3/2)} ?

The first derivative of 9/(4(3x+2)^{3/2)} is -(81)/(8(3x+2)^{5/2)}

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derivative of

\frac{9}{4 ( 3 x + 2 ) ^{\frac{3}{2}}}

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

Solution steps

\frac{d}{d x} (\frac{9}{4 ( 3 x + 2 ) ^{\frac{3}{2}}})

Take the constant out:

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

= \frac{9}{4} \frac{d}{d x} (\frac{1}{( 3 x + 2 ) ^{\frac{3}{2}}})

Apply exponent rule:

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

= \frac{9}{4} \frac{d}{d x} ((3 x + 2)^{- \frac{3}{2}})

Apply the chain rule:

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

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

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

= \frac{9}{4} (- \frac{3}{2 ( 3 x + 2 ) ^{\frac{5}{2}}} \cdot 3)

Simplify

\frac{9}{4} (- \frac{3}{2 ( 3 x + 2 ) ^{\frac{5}{2}}} \cdot 3) : - \frac{81}{8 ( 3 x + 2 ) ^{\frac{5}{2}}}

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

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What is the derivative of 9/(4(3x+2)^{3/2)} ?
The derivative of 9/(4(3x+2)^{3/2)} is -(81)/(8(3x+2)^{5/2)}
What is the first derivative of 9/(4(3x+2)^{3/2)} ?
The first derivative of 9/(4(3x+2)^{3/2)} is -(81)/(8(3x+2)^{5/2)}