What is the derivative of 4/(x-5) ?

The derivative of 4/(x-5) is -4/((x-5)^2)

What is the first derivative of 4/(x-5) ?

The first derivative of 4/(x-5) is -4/((x-5)^2)

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derivative of

\frac{4}{x - 5}

- \frac{4}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4}{x - 5})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{x - 5})

Apply exponent rule:

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

= 4 \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

= 4 (- \frac{1}{( x - 5 ) ^{2}} \cdot 1)

Simplify

4 (- \frac{1}{( x - 5 ) ^{2}} \cdot 1) : - \frac{4}{( x - 5 ) ^{2}}

= - \frac{4}{( x - 5 ) ^{2}}

\frac{\partial}{\partial x} (\frac{x}{y + 2 z})

\int e^{- \frac{y}{2}} d y

sin (x) + 5 π x

\frac{1}{8} (e^{4 x} + e^{- 4 x})

\int x 4 x^{2} + 5 d x

What is the derivative of 4/(x-5) ?
The derivative of 4/(x-5) is -4/((x-5)^2)
What is the first derivative of 4/(x-5) ?
The first derivative of 4/(x-5) is -4/((x-5)^2)