What is the derivative of (1/(x-3)^2) ?

The derivative of (1/(x-3)^2) is -2/((x-3)^3)

What is the first derivative of (1/(x-3)^2) ?

The first derivative of (1/(x-3)^2) is -2/((x-3)^3)

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

- \frac{2}{( x - 3 ) ^{3}}

Solution steps

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

Apply the chain rule:

2 \cdot \frac{1}{x - 3} \frac{d}{d x} (\frac{1}{x - 3})

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

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

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

Simplify

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

= - \frac{2}{( x - 3 ) ^{3}}

What is the derivative of (1/(x-3)^2) ?
The derivative of (1/(x-3)^2) is -2/((x-3)^3)
What is the first derivative of (1/(x-3)^2) ?
The first derivative of (1/(x-3)^2) is -2/((x-3)^3)