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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{1}{x} e^{x} d x

f (x) = \frac{4 x ^{2} + 6 x + 6}{x}

\int e^{- 2 x} cos (4 x) d x

\int \frac{1}{48 x + 6 x ^{2}} d x

x \to 6 lim (8 x^{2} - 7 x + 1)

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