What is the derivative of f(x)= 4/((3x)^{-2)} ?

The derivative of f(x)= 4/((3x)^{-2)} is 72x

What is the first derivative of f(x)= 4/((3x)^{-2)} ?

The first derivative of f(x)= 4/((3x)^{-2)} is 72x

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derivative of

f (x) = \frac{4}{( 3 x ) ^{- 2}}

72 x

Solution steps

\frac{d}{d x} (\frac{4}{( 3 x ) ^{- 2}})

Take the constant out:

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

= 4 \frac{d}{d x} (\frac{1}{( 3 x ) ^{- 2}})

Apply exponent rule:

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

= 4 \frac{d}{d x} ((3 x)^{2})

Apply the chain rule:

2 \cdot 3 x \frac{d}{d x} (3 x)

= 2 \cdot 3 x \frac{d}{d x} (3 x)

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

= 4 \cdot 2 \cdot 3 x \cdot 3

Simplify

= 72 x

\int \frac{5}{x ^{- 1} + 5} d x

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\frac{d}{d x} (\frac{7 x ^{2}}{x})

\int_{0}^{1} 9 (x^{2} + 1) e^{- x} d x

\int \frac{x}{2 x + 3} d x

What is the derivative of f(x)= 4/((3x)^{-2)} ?
The derivative of f(x)= 4/((3x)^{-2)} is 72x
What is the first derivative of f(x)= 4/((3x)^{-2)} ?
The first derivative of f(x)= 4/((3x)^{-2)} is 72x