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

The derivative of (12)/(6x^2+1) is -(144x)/((6x^2+1)^2)

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

The first derivative of (12)/(6x^2+1) is -(144x)/((6x^2+1)^2)

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derivative of

\frac{12}{6 x ^{2} + 1}

- \frac{144 x}{( 6 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{12}{6 x ^{2} + 1})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (\frac{1}{6 x ^{2} + 1})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 x^{2} + 1) = 12 x

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

Simplify

12 (- \frac{1}{( 6 x ^{2} + 1 ) ^{2}} \cdot 12 x) : - \frac{144 x}{( 6 x ^{2} + 1 ) ^{2}}

= - \frac{144 x}{( 6 x ^{2} + 1 ) ^{2}}

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What is the derivative of (12)/(6x^2+1) ?
The derivative of (12)/(6x^2+1) is -(144x)/((6x^2+1)^2)
What is the first derivative of (12)/(6x^2+1) ?
The first derivative of (12)/(6x^2+1) is -(144x)/((6x^2+1)^2)