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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{( x - 5 ) ^{2}} \frac{d}{d x} (x - 5)

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

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

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

Simplify

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

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

y = x^{2} + 8

x \to 0 + lim (cot (3 x))

\frac{\partial}{\partial y} (3 x y^{2})

\frac{d}{d x} (\frac{tan ( 3 x )}{x ^{2}})

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