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

The derivative of ((-2))/((2x+1)^2) is 8/((2x+1)^3)

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

The first derivative of ((-2))/((2x+1)^2) is 8/((2x+1)^3)

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derivative of

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

\frac{8}{( 2 x + 1 ) ^{3}}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply exponent rule:

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

= - 2 \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

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

Simplify

- 2 (- \frac{2}{( 2 x + 1 ) ^{3}} \cdot 2) : \frac{8}{( 2 x + 1 ) ^{3}}

= \frac{8}{( 2 x + 1 ) ^{3}}

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

sin (x^{6}) + sin^{6} (x)

\frac{10 x}{( x + 7 )}

3 - x

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

What is the derivative of ((-2))/((2x+1)^2) ?
The derivative of ((-2))/((2x+1)^2) is 8/((2x+1)^3)
What is the first derivative of ((-2))/((2x+1)^2) ?
The first derivative of ((-2))/((2x+1)^2) is 8/((2x+1)^3)