What is the derivative of y=(1/(2x+1)-2)^3 ?

The derivative of y=(1/(2x+1)-2)^3 is -(6(-4x-1)^2)/((2x+1)^4)

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

The first derivative of y=(1/(2x+1)-2)^3 is -(6(-4x-1)^2)/((2x+1)^4)

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derivative of

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

- \frac{6 ( - 4 x - 1 ) ^{2}}{( 2 x + 1 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

3 (\frac{1}{2 x + 1} - 2)^{2} (- \frac{2}{( 2 x + 1 ) ^{2}}) : - \frac{6 ( - 4 x - 1 ) ^{2}}{( 2 x + 1 ) ^{4}}

= - \frac{6 ( - 4 x - 1 ) ^{2}}{( 2 x + 1 ) ^{4}}

\frac{d}{d x} (ln (e^{7 x}))

x \to - 3 lim (- 1)

\int \frac{1}{( x + 4 ) x ^{2} + 8 x} d x

b e^{x}

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

What is the derivative of y=(1/(2x+1)-2)^3 ?
The derivative of y=(1/(2x+1)-2)^3 is -(6(-4x-1)^2)/((2x+1)^4)
What is the first derivative of y=(1/(2x+1)-2)^3 ?
The first derivative of y=(1/(2x+1)-2)^3 is -(6(-4x-1)^2)/((2x+1)^4)