What is the derivative of f(x)=(36)/((1+3x)^3) ?

The derivative of f(x)=(36)/((1+3x)^3) is -(324)/((1+3x)^4)

What is the first derivative of f(x)=(36)/((1+3x)^3) ?

The first derivative of f(x)=(36)/((1+3x)^3) is -(324)/((1+3x)^4)

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derivative of

f (x) = \frac{36}{( 1 + 3 x ) ^{3}}

- \frac{324}{( 1 + 3 x ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{36}{( 1 + 3 x ) ^{3}})

Take the constant out:

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

= 36 \frac{d}{d x} (\frac{1}{( 1 + 3 x ) ^{3}})

Apply exponent rule:

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

= 36 \frac{d}{d x} ((1 + 3 x)^{- 3})

Apply the chain rule:

- \frac{3}{( 1 + 3 x ) ^{4}} \frac{d}{d x} (1 + 3 x)

= - \frac{3}{( 1 + 3 x ) ^{4}} \frac{d}{d x} (1 + 3 x)

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

= 36 (- \frac{3}{( 1 + 3 x ) ^{4}} \cdot 3)

Simplify

36 (- \frac{3}{( 1 + 3 x ) ^{4}} \cdot 3) : - \frac{324}{( 1 + 3 x ) ^{4}}

= - \frac{324}{( 1 + 3 x ) ^{4}}

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What is the derivative of f(x)=(36)/((1+3x)^3) ?
The derivative of f(x)=(36)/((1+3x)^3) is -(324)/((1+3x)^4)
What is the first derivative of f(x)=(36)/((1+3x)^3) ?
The first derivative of f(x)=(36)/((1+3x)^3) is -(324)/((1+3x)^4)