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Differentiation problem

How do you solve this:

Find the derivative of the function given y=[(x^3-6)^6]/[(1-3x^2)^5]

I got stuck… hahaha

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Answer #1

You need to use a couple of rules to make it easier. First the chain rule (for simplification) and then the quotient rule.

(Warning! This is gonna be a huge answer and will look very confusing on this page).

let g(x) = (x^3 - 6)^6 and let h(x) = (1 - 3x^2)^5 therefore g’(x) = 18(x^2)(x^3 - 6)^d and h’(x) = -15x(1-3x^2)^4

and why can be written as y = g(x) / h(x). Then using the quotient rule, dy/dx = [h(x)g’(x) - g(x)h’(x)] / [h(x)]^2 Just make the appropriate substitutions into the above formulae and you should get the correct answer. I would do it myself but it’s really annoying to do on the computer. Sorry hehe. Hope this helped.

Answer #2

Alternatively, you can rewrite why as y = [(x^3-6)^6][(1-3x^2)^-5] and use the chain and product rules of differentiation instead. Same thing really but it’s easier to manage then my previous answer.

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