What is the derivative of (16/((2x+1)^3)) ?

The derivative of (16/((2x+1)^3)) is -(96)/((2x+1)^4)

What is the first derivative of (16/((2x+1)^3)) ?

The first derivative of (16/((2x+1)^3)) is -(96)/((2x+1)^4)

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\frac{d}{d x} (\frac{16}{( 2 x + 1 ) ^{3}})

- \frac{96}{( 2 x + 1 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{16}{( 2 x + 1 ) ^{3}})

Take the constant out:

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

= 16 \frac{d}{d x} (\frac{1}{( 2 x + 1 ) ^{3}})

Apply exponent rule:

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

= 16 \frac{d}{d x} ((2 x + 1)^{- 3})

Apply the chain rule:

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

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

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

= 16 (- \frac{3}{( 2 x + 1 ) ^{4}} \cdot 2)

Simplify

16 (- \frac{3}{( 2 x + 1 ) ^{4}} \cdot 2) : - \frac{96}{( 2 x + 1 ) ^{4}}

= - \frac{96}{( 2 x + 1 ) ^{4}}

What is the derivative of (16/((2x+1)^3)) ?
The derivative of (16/((2x+1)^3)) is -(96)/((2x+1)^4)
What is the first derivative of (16/((2x+1)^3)) ?
The first derivative of (16/((2x+1)^3)) is -(96)/((2x+1)^4)