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

The derivative of 1/(6x^2+5) is -(12x)/((6x^2+5)^2)

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

The first derivative of 1/(6x^2+5) is -(12x)/((6x^2+5)^2)

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derivative of

\frac{1}{6 x ^{2} + 5}

- \frac{12 x}{( 6 x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{6 x ^{2} + 5})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 x^{2} + 5) = 12 x

= - \frac{1}{( 6 x ^{2} + 5 ) ^{2}} \cdot 12 x

Simplify

- \frac{1}{( 6 x ^{2} + 5 ) ^{2}} \cdot 12 x : - \frac{12 x}{( 6 x ^{2} + 5 ) ^{2}}

= - \frac{12 x}{( 6 x ^{2} + 5 ) ^{2}}

What is the derivative of 1/(6x^2+5) ?
The derivative of 1/(6x^2+5) is -(12x)/((6x^2+5)^2)
What is the first derivative of 1/(6x^2+5) ?
The first derivative of 1/(6x^2+5) is -(12x)/((6x^2+5)^2)