What is the derivative of f(x)=(20)/((x+3)^2) ?

The derivative of f(x)=(20)/((x+3)^2) is -(40)/((x+3)^3)

What is the first derivative of f(x)=(20)/((x+3)^2) ?

The first derivative of f(x)=(20)/((x+3)^2) is -(40)/((x+3)^3)

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derivative of

f (x) = \frac{20}{( x + 3 ) ^{2}}

- \frac{40}{( x + 3 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{20}{( x + 3 ) ^{2}})

Take the constant out:

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

= 20 \frac{d}{d x} (\frac{1}{( x + 3 ) ^{2}})

Apply exponent rule:

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

= 20 \frac{d}{d x} ((x + 3)^{- 2})

Apply the chain rule:

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

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

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

= 20 (- \frac{2}{( x + 3 ) ^{3}} \cdot 1)

Simplify

20 (- \frac{2}{( x + 3 ) ^{3}} \cdot 1) : - \frac{40}{( x + 3 ) ^{3}}

= - \frac{40}{( x + 3 ) ^{3}}

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What is the derivative of f(x)=(20)/((x+3)^2) ?
The derivative of f(x)=(20)/((x+3)^2) is -(40)/((x+3)^3)
What is the first derivative of f(x)=(20)/((x+3)^2) ?
The first derivative of f(x)=(20)/((x+3)^2) is -(40)/((x+3)^3)