What is the derivative of 5/(x-3) ?

The derivative of 5/(x-3) is -5/((x-3)^2)

What is the first derivative of 5/(x-3) ?

The first derivative of 5/(x-3) is -5/((x-3)^2)

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\frac{d}{d x} (\frac{5}{x - 3})

- \frac{5}{( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5}{x - 3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (\frac{1}{x - 3})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((x - 3)^{- 1})

Apply the chain rule:

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

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

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

= 5 (- \frac{1}{( x - 3 ) ^{2}} \cdot 1)

Simplify

5 (- \frac{1}{( x - 3 ) ^{2}} \cdot 1) : - \frac{5}{( x - 3 ) ^{2}}

= - \frac{5}{( x - 3 ) ^{2}}

What is the derivative of 5/(x-3) ?
The derivative of 5/(x-3) is -5/((x-3)^2)
What is the first derivative of 5/(x-3) ?
The first derivative of 5/(x-3) is -5/((x-3)^2)