What is the derivative of f(r)= 5/(r^3) ?

The derivative of f(r)= 5/(r^3) is -(15)/(r^4)

What is the first derivative of f(r)= 5/(r^3) ?

The first derivative of f(r)= 5/(r^3) is -(15)/(r^4)

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derivative of

f (r) = \frac{5}{r ^{3}}

- \frac{15}{r ^{4}}

Solution steps

\frac{d}{d r} (\frac{5}{r ^{3}})

Take the constant out:

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

= 5 \frac{d}{d r} (\frac{1}{r ^{3}})

Apply exponent rule:

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

= 5 \frac{d}{d r} (r^{- 3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5 (- 3 r^{- 3 - 1})

Simplify

5 (- 3 r^{- 3 - 1}) : - \frac{15}{r ^{4}}

= - \frac{15}{r ^{4}}

What is the derivative of f(r)= 5/(r^3) ?
The derivative of f(r)= 5/(r^3) is -(15)/(r^4)
What is the first derivative of f(r)= 5/(r^3) ?
The first derivative of f(r)= 5/(r^3) is -(15)/(r^4)