C1 2015 3 Edexcel

3

Write y = 4x^3 - 5x^{-2}.

(a)

We have:

\begin{align*}\frac {\mathrm dy} {\mathrm dx} & = 12x^2 + 10x^{-3} \\ & = 12x^2 + \frac {10} {x^3}\end{align*}

(b)

We have:

\begin{align*}\int y \mathrm dx & = \frac {4x^{3 + 1}} {3 + 1} - \frac {5x^{-2 + 1}} {-2 + 1} + C \\ & = x^4 + 5x^{-1} + C\\ & = x^4 + \frac 5 x + C\end{align*}

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