What is the derivative of 1/(3x^2+5x) ?

The derivative of 1/(3x^2+5x) is -(6x+5)/((3x^2+5x)^2)

What is the first derivative of 1/(3x^2+5x) ?

The first derivative of 1/(3x^2+5x) is -(6x+5)/((3x^2+5x)^2)

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\frac{d}{d x} (\frac{1}{3 x ^{2} + 5 x})

- \frac{6 x + 5}{( 3 x ^{2} + 5 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{3 x ^{2} + 5 x})

Apply exponent rule:

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

= \frac{d}{d x} ((3 x^{2} + 5 x)^{- 1})

Apply the chain rule:

- \frac{1}{( 3 x ^{2} + 5 x ) ^{2}} \frac{d}{d x} (3 x^{2} + 5 x)

= - \frac{1}{( 3 x ^{2} + 5 x ) ^{2}} \frac{d}{d x} (3 x^{2} + 5 x)

\frac{d}{d x} (3 x^{2} + 5 x) = 6 x + 5

= - \frac{1}{( 3 x ^{2} + 5 x ) ^{2}} (6 x + 5)

Simplify

- \frac{1}{( 3 x ^{2} + 5 x ) ^{2}} (6 x + 5) : - \frac{6 x + 5}{( 3 x ^{2} + 5 x ) ^{2}}

= - \frac{6 x + 5}{( 3 x ^{2} + 5 x ) ^{2}}

What is the derivative of 1/(3x^2+5x) ?
The derivative of 1/(3x^2+5x) is -(6x+5)/((3x^2+5x)^2)
What is the first derivative of 1/(3x^2+5x) ?
The first derivative of 1/(3x^2+5x) is -(6x+5)/((3x^2+5x)^2)