Math CentralQuandaries & Queries


Question from joey, a student:

pls help me to Differentiate


Hi Joey,

I'm going to solve a similar problem.

Differentiate y = (1/2 x3 - x2 + 3)6

This is an application of the chain rule. What you need to see is that this is a function f(x), raised to a power. You have f(x) = 1/2 x3 - x2 + 3 raised to the sixth power. The chain rule for functions of the form [f(x)]n states that

If y = [f(x)]n then dy/dx = n[f(x)]n-1 × f '(x)

In my problem n = 6 and f(x) = 1/2 x3 - x2 + 3 so f '(x) = 3/2 x2 - 2x. Thus

dy/dx = 6 [1/2 x3 - x2 + 3]5 × (3/2 x2 - 2x)

Now try your problem,

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