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C4 differentiation

EL77

Can I use the chain rule to differentiate this function with respect to x?

(xy)^1/2

Reply 1

EL77

I'd have thought you would use the product rule

(edited 10 years ago)

Reply 2

Hasufel

yup. use also product rule for implicitly differentiating the "xy"

Reply 3

EL77

Original post by Hasufel

yup. use also product rule for implicitly differentiating the "xy"

oh okay so because the whole thing is to the power of a half I can use the chain rule? i would have thought you would have to use the product rule throughout?

Reply 4

Hasufel

both.

\frac{d}{dx} (xy)^{1/2}=\frac{d}{dx}(u)^{1/2}=(\frac{1}{2}u^{-1/2})\frac{du}{dx}

and for du/dx =

\frac{d}{dx}(xy)

implicitly

Reply 5

Hasufel

you can split it, (x^(1/2)y^(1/2)) and use the product rule, but there`s too many fractional powers for my liking (personal taste)

Reply 6

EL77

but then if that can be done by the chain rule, that would mean you could differentiate xy by the chain rule, but you would need to use the product rule to differentiate xy

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C4 differentiation

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