What is the derivative of 1/(4x-7) ?

The derivative of 1/(4x-7) is -4/((4x-7)^2)

What is the first derivative of 1/(4x-7) ?

The first derivative of 1/(4x-7) is -4/((4x-7)^2)

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\frac{d}{d x} (\frac{1}{4 x - 7})

- \frac{4}{( 4 x - 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{4 x - 7})

Apply exponent rule:

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

= \frac{d}{d x} ((4 x - 7)^{- 1})

Apply the chain rule:

- \frac{1}{( 4 x - 7 ) ^{2}} \frac{d}{d x} (4 x - 7)

= - \frac{1}{( 4 x - 7 ) ^{2}} \frac{d}{d x} (4 x - 7)

\frac{d}{d x} (4 x - 7) = 4

= - \frac{1}{( 4 x - 7 ) ^{2}} \cdot 4

Simplify

- \frac{1}{( 4 x - 7 ) ^{2}} \cdot 4 : - \frac{4}{( 4 x - 7 ) ^{2}}

= - \frac{4}{( 4 x - 7 ) ^{2}}

What is the derivative of 1/(4x-7) ?
The derivative of 1/(4x-7) is -4/((4x-7)^2)
What is the first derivative of 1/(4x-7) ?
The first derivative of 1/(4x-7) is -4/((4x-7)^2)