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Popular >

derivative of 1/(6x-7)

Solution

\frac{d}{d x} (\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}}

Popular Examples

limit as x approaches-1 of 3x^2-3x+3

x \to - 1 lim (3 x^{2} - 3 x + 3)

derivative of (-1^nx^n)

\frac{d}{d x} ((- 1)^{n} x^{n})

integral of 1/(x^4)-1/(\sqrt[4]{x)}+4

derivative of (1+sqrt(x)/x)

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

y^{''}+2y^'-3y=0,y(0)=4,y^'(0)=1

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 4, y^{^{'}} (0) = 1

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)