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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 5 x^{3} (x - 5)^{- 4} d x

\frac{s + 2}{( s - 1 ) ( s + 6 )}

2 x, x^{2} - 4 x

y^{^{'}} + 2 y = x^{2} + 2 x

\int_{0}^{1} \frac{2 x}{( x ^{2} + 2 ) ^{3}} d x

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