When to use the product Rule: For f(x) = 1/sqrt{2x^2 - 3x}, find f'(x).

[jonoweight]

Hi,

I am having trouble seeing why the questions asks to use the product rule here. Is this equation a product of 2 functions?

If someone could please shed some light that would be great.

Thanks!

 

[stapel]

View attachment 36986
Hi,

I am having trouble seeing why the questions asks to use the product rule here. Is this equation a product of 2 functions?

If someone could please shed some light that would be great.

They seem to be going out of their way to make this complicated. Do they maybe mean the following?

[imath]\qquad f(x) = (1)(\sqrt{2x^2 - 3x\,})^{-1}[/imath]

Or do they maybe mean that you're supposed to use the Chain Rule, differentiating the square root and then differentiating the insides?

My guess would be the latter, but check with your instructor to be sure.

 

[blamocur]

My guess would be the latter, but check with your instructor to be sure.

That would be my guess too, i.e. that by 'product' they mean composition of two functions: [imath]f(u)=\frac{1}{\sqrt{u}}[/imath] and [imath]u(x) = 2x^2-3x[/imath].

 

[fresh_42]

[imath] 2x^2-3x=x(2x-3) [/imath] is the only place where the product rule can be applied. [imath] f(u)=\sqrt{u}^{-1} [/imath] requires the chain rule.