What is the derivative of f(x)= 4/(x+4) ?

The derivative of f(x)= 4/(x+4) is -4/((x+4)^2)

What is the first derivative of f(x)= 4/(x+4) ?

The first derivative of f(x)= 4/(x+4) is -4/((x+4)^2)

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derivative of

f (x) = \frac{4}{x + 4}

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

Solution steps

\frac{d}{d x} (\frac{4}{x + 4})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{x + 4})

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{( x + 4 ) ^{2}} \frac{d}{d x} (x + 4)

= - \frac{1}{( x + 4 ) ^{2}} \frac{d}{d x} (x + 4)

\frac{d}{d x} (x + 4) = 1

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

Simplify

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

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

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