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Popular Calculus >

derivative of 1+a/r-b/(r^3)

Solution

derivative of

1 + \frac{a}{r} - \frac{b}{r ^{3}}

Solution

\frac{3 b}{r ^{4}} - \frac{a}{r ^{2}}

Solution steps

\frac{d}{d r} (1 + \frac{a}{r} - \frac{b}{r ^{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d r} (1) + \frac{d}{d r} (\frac{a}{r}) - \frac{d}{d r} (\frac{b}{r ^{3}})

\frac{d}{d r} (1) = 0

\frac{d}{d r} (\frac{a}{r}) = - \frac{a}{r ^{2}}

\frac{d}{d r} (\frac{b}{r ^{3}}) = - \frac{3 b}{r ^{4}}

= 0 - \frac{a}{r ^{2}} - (- \frac{3 b}{r ^{4}})

Simplify

= \frac{3 b}{r ^{4}} - \frac{a}{r ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 1+a/r-b/(r^3) ?
The derivative of 1+a/r-b/(r^3) is (3b)/(r^4)-a/(r^2)
What is the first derivative of 1+a/r-b/(r^3) ?
The first derivative of 1+a/r-b/(r^3) is (3b)/(r^4)-a/(r^2)