Log functions question (1 Viewer)

MilkDrinker · Dec 4, 2012

Hi guys, I need help understanding the solution to a question.

This was a former HSC question, I don't understand one aspect of the solutions.

QUestion: If $y=10^x$ , find y' when x=1

Answers:
$y=10^x\therefore lny=xln10\\\frac{d}{dx}(lny)=\frac{d}{dx}(x ln 10)\\\mathbf{\frac{1}{y} \\\frac{dy}{dx}=ln 10}\\\frac{dy}{dx}=yln10= 10^x ln 10\\\therefore at x=1, \frac{dy}{dx}=10ln10$
I dont understand the line in bold.
where did the dy/dx come from

please ignore the random <br/> through it

please explain. Thanks

Shadowdude · Dec 4, 2012

I believe that's just an application of the chain rule.

D94 · Dec 4, 2012

It's differentiation where y is a function of x, but essentially, d(lny)/dx = d(lny)/dy * dy/dx. So d/dy = 1/y and you multiply this by dy/dx, hence 1/y * dy/dx.

Carrotsticks · Dec 4, 2012

MilkDrinker · Dec 4, 2012

Thanks guys so much... That was very useful :d

Log functions question (1 Viewer)

MilkDrinker

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Shadowdude

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D94

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Carrotsticks

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MilkDrinker

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