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

The derivative of (-2/(3x+7)) is 6/((3x+7)^2)

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

The first derivative of (-2/(3x+7)) is 6/((3x+7)^2)

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

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

Solution steps

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

Simplify

\frac{- 2}{3 x + 7} : - \frac{2}{3 x + 7}

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

- 2 (- \frac{1}{( 3 x + 7 ) ^{2}} \cdot 3) : \frac{6}{( 3 x + 7 ) ^{2}}

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

What is the derivative of (-2/(3x+7)) ?
The derivative of (-2/(3x+7)) is 6/((3x+7)^2)
What is the first derivative of (-2/(3x+7)) ?
The first derivative of (-2/(3x+7)) is 6/((3x+7)^2)