What is the derivative of 1/(4x^2+2x) ?

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

What is the first derivative of 1/(4x^2+2x) ?

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

= - \frac{1}{( 4 x ^{2} + 2 x ) ^{2}} (8 x + 2)

Simplify

- \frac{1}{( 4 x ^{2} + 2 x ) ^{2}} (8 x + 2) : - \frac{4 x + 1}{2 x ^{2} ( 2 x + 1 ) ^{2}}

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

x \to 2 lim (2 + 3)

\frac{d}{d x} (\frac{x ^{3} + 3 x ^{2} - 5 x + 2}{3})

y^{^{'''}} - 2 y^{^{''}} - 3 y^{^{'}} = 0

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

\int e^{4 x} sin (x) d x

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