What is the derivative of f(x)= 5/(x+5) ?

The derivative of f(x)= 5/(x+5) is -5/((x+5)^2)

What is the first derivative of f(x)= 5/(x+5) ?

The first derivative of f(x)= 5/(x+5) is -5/((x+5)^2)

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derivative of

f (x) = \frac{5}{x + 5}

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

Solution steps

\frac{d}{d x} (\frac{5}{x + 5})

Take the constant out:

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

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

Apply exponent rule:

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

= 5 \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

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

Simplify

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

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

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