What is the derivative of (11/((2x+1)^2)) ?

The derivative of (11/((2x+1)^2)) is -(44)/((2x+1)^3)

What is the first derivative of (11/((2x+1)^2)) ?

The first derivative of (11/((2x+1)^2)) is -(44)/((2x+1)^3)

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\frac{d}{d x} (\frac{11}{( 2 x + 1 ) ^{2}})

- \frac{44}{( 2 x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{11}{( 2 x + 1 ) ^{2}})

Take the constant out:

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

= 11 \frac{d}{d x} (\frac{1}{( 2 x + 1 ) ^{2}})

Apply exponent rule:

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

= 11 \frac{d}{d x} ((2 x + 1)^{- 2})

Apply the chain rule:

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

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

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

= 11 (- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2)

Simplify

11 (- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2) : - \frac{44}{( 2 x + 1 ) ^{3}}

= - \frac{44}{( 2 x + 1 ) ^{3}}

What is the derivative of (11/((2x+1)^2)) ?
The derivative of (11/((2x+1)^2)) is -(44)/((2x+1)^3)
What is the first derivative of (11/((2x+1)^2)) ?
The first derivative of (11/((2x+1)^2)) is -(44)/((2x+1)^3)