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  • 01-05-2017
  • Mathematics
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if f(x) is a function whose derivative is f'(x)=1/x, find the derivative of the function y=xf(x)-x

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jdoe0001 jdoe0001
  • 01-05-2017
[tex]\bf \textit{let's make }f(x)=z\qquad thus\quad z'(x)=\cfrac{1}{x}\\\\ \textit{for the sake of disambiguiting it some} \\\\ -----------------------------\\\\ y=xz-x\impliedby \textit{using the product rule} \\\\\\ \cfrac{dy}{dx}=[1\cdot z+x\cdot \frac{dz}{dx}]-1\implies \cfrac{dy}{dx}=z+x\cdot \cfrac{1}{x}-1\implies \cfrac{dy}{dx}=z[/tex]
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