What is the derivative of 6(x^2+3)^{-1} ?

The derivative of 6(x^2+3)^{-1} is -(12x)/((x^2+3)^2)

What is the first derivative of 6(x^2+3)^{-1} ?

The first derivative of 6(x^2+3)^{-1} is -(12x)/((x^2+3)^2)

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derivative of

6 (x^{2} + 3)^{- 1}

- \frac{12 x}{( x ^{2} + 3 ) ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

6 (- \frac{1}{( x ^{2} + 3 ) ^{2}} \cdot 2 x) : - \frac{12 x}{( x ^{2} + 3 ) ^{2}}

= - \frac{12 x}{( x ^{2} + 3 ) ^{2}}

y = x^{2} \cdot (x + 1)^{3}

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\frac{d}{dd} (ln (\frac{ln ( 8 l )}{d}) - 1)

12 x - 4

3 tan (x) - 4 cot (x_{7}) x^{2}

What is the derivative of 6(x^2+3)^{-1} ?
The derivative of 6(x^2+3)^{-1} is -(12x)/((x^2+3)^2)
What is the first derivative of 6(x^2+3)^{-1} ?
The first derivative of 6(x^2+3)^{-1} is -(12x)/((x^2+3)^2)