y=1x^3 y=x^ 3 Differentiating w.r.t x #160; ddx y=ddxx^ 3 dydx= 3x^ 4 dydx= 3x^4 ...

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Integration as Antiderivative

If y= 1 x3 ...

Question

If $y = \frac{1}{x^{3}}$ find $\frac{d y}{d x}$

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Solution

$y = \frac{1}{x^{3}} y = x^{- 3}$
Differentiating w.r.t x
$\frac{d}{d x} y = \frac{d}{d x} x^{- 3} \frac{d y}{d x} = - 3 x^{- 4} \frac{d y}{d x} = \frac{- 3}{x^{4}}$

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