What is the derivative of g(x)= 1/(4x^2+5x) ?

The derivative of g(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)

What is the first derivative of g(x)= 1/(4x^2+5x) ?

The first derivative of g(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)

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derivative of

g (x) = \frac{1}{4 x ^{2} + 5 x}

- \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{4 x ^{2} + 5 x})

Apply exponent rule:

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

= \frac{d}{d x} ((4 x^{2} + 5 x)^{- 1})

Apply the chain rule:

- \frac{1}{( 4 x ^{2} + 5 x ) ^{2}} \frac{d}{d x} (4 x^{2} + 5 x)

= - \frac{1}{( 4 x ^{2} + 5 x ) ^{2}} \frac{d}{d x} (4 x^{2} + 5 x)

\frac{d}{d x} (4 x^{2} + 5 x) = 8 x + 5

= - \frac{1}{( 4 x ^{2} + 5 x ) ^{2}} (8 x + 5)

Simplify

- \frac{1}{( 4 x ^{2} + 5 x ) ^{2}} (8 x + 5) : - \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

= - \frac{8 x + 5}{( 4 x ^{2} + 5 x ) ^{2}}

sin (5 t - \frac{π}{3}) \cdot 1 (5 t - \frac{π}{3})

\frac{3 z - 5}{z ^{2} - 4 z + 3}

\int_{1}^{3} \frac{e ^{\frac{3}{x}}}{x ^{2}} d x

(3 x + 2 y) d x + (2 x + y) d y = 0

\frac{\partial}{\partial x} (\frac{x + y}{z})

What is the derivative of g(x)= 1/(4x^2+5x) ?
The derivative of g(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)
What is the first derivative of g(x)= 1/(4x^2+5x) ?
The first derivative of g(x)= 1/(4x^2+5x) is -(8x+5)/((4x^2+5x)^2)