What is the derivative of 2/((3x^2+7^2)) ?

The derivative of 2/((3x^2+7^2)) is -(24x)/((3x^2+7)^3)

What is the first derivative of 2/((3x^2+7^2)) ?

The first derivative of 2/((3x^2+7^2)) is -(24x)/((3x^2+7)^3)

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\frac{d}{d x} (\frac{2}{( 3 x ^{2} + 7 ) ^{2}})

- \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2}{( 3 x ^{2} + 7 ) ^{2}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{( 3 x ^{2} + 7 ) ^{2}})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((3 x^{2} + 7)^{- 2})

Apply the chain rule:

- \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \frac{d}{d x} (3 x^{2} + 7)

= - \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \frac{d}{d x} (3 x^{2} + 7)

\frac{d}{d x} (3 x^{2} + 7) = 6 x

= 2 (- \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \cdot 6 x)

Simplify

2 (- \frac{2}{( 3 x ^{2} + 7 ) ^{3}} \cdot 6 x) : - \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}}

= - \frac{24 x}{( 3 x ^{2} + 7 ) ^{3}}

What is the derivative of 2/((3x^2+7^2)) ?
The derivative of 2/((3x^2+7^2)) is -(24x)/((3x^2+7)^3)
What is the first derivative of 2/((3x^2+7^2)) ?
The first derivative of 2/((3x^2+7^2)) is -(24x)/((3x^2+7)^3)