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Popular >

derivative of 1/(6x+7)

Solution

derivative of

\frac{1}{6 x + 7}

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{6 x + 7})

Apply exponent rule:

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

= \frac{d}{d x} ((6 x + 7)^{- 1})

Apply the chain rule:

- \frac{1}{( 6 x + 7 ) ^{2}} \frac{d}{d x} (6 x + 7)

= - \frac{1}{( 6 x + 7 ) ^{2}} \frac{d}{d x} (6 x + 7)

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of 1/(6x+7) ?
The derivative of 1/(6x+7) is -6/((6x+7)^2)
What is the first derivative of 1/(6x+7) ?
The first derivative of 1/(6x+7) is -6/((6x+7)^2)