What is the derivative of 3/((2x+3)^2) ?

The derivative of 3/((2x+3)^2) is -(12)/((2x+3)^3)

What is the first derivative of 3/((2x+3)^2) ?

The first derivative of 3/((2x+3)^2) is -(12)/((2x+3)^3)

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derivative of

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

- \frac{12}{( 2 x + 3 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 (- \frac{2}{( 2 x + 3 ) ^{3}} \cdot 2) : - \frac{12}{( 2 x + 3 ) ^{3}}

= - \frac{12}{( 2 x + 3 ) ^{3}}

x \to \infty lim (- 1^{- x})

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

\frac{d}{d x} (\frac{3 x - 9}{2 x + 8})

\int_{0}^{\frac{π}{6}} sec^{2} (x) d x

f (x) = x^{3} + 2 x

What is the derivative of 3/((2x+3)^2) ?
The derivative of 3/((2x+3)^2) is -(12)/((2x+3)^3)
What is the first derivative of 3/((2x+3)^2) ?
The first derivative of 3/((2x+3)^2) is -(12)/((2x+3)^3)