I'm having trouble getting to the derivative of $\displaystyle y = x^2 sqrt(x-2)$. Could someone kindly provide a step-by-step solution to the problem? The answer is $\displaystyle x(5x - 8) / 2 sqrt(x-2)$
Are you sure? Here's a pic - I'll edit details and quite possibly corrections...
Actually, the chain rule here is kind of trivial, so we could just use the product rule alone...
... where...
... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and then, because of the product rule, the whole of the bottom is the derivative of the whole of the top.
Notice I've tweaked the second balloon along the bottom, just for a common denominator.
OK - where does that get us in view of your proposed answer? Have you checked question and answer? Maybe its me...
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Don't integrate - balloontegrate!
http://www.ballooncalculus.org/examples/gallery.html
http://www.ballooncalculus.org/asy/doc.html
Sorry, should have thought to do an additional tweak for the same reason, then I wouldn't have been confused...
So, yes, there we are. Maybe your mental blip was related to mine. Anyway, hope you like the balloons for tracing through the product rule process - if not, use the formula, of course.