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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

arctan (cos (3 x))

\int \frac{x - 1}{x ^{3}} d x

f (y) = 2 e^{y}

x \to - 4 lim (\frac{\frac{4}{x} + 1}{x + 4})

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

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