Given that f(x)= (3+x^2)(x^1/2-7x). Find f'(x) (5marks)
Because there are two functions that are enclosed in brackets, you should realise that you need to differentiate by parts. You can expand out and differentiate through, but because of the x^1/2 it can get quite complicated and messy. Step 1. define f(x) and g(x)h(x)=3+x^2 g(x)=x^1/2-7xNow differentiate both of those separatelyh'(x)=2xg'(x)=1/2x^-1/2x-7It is worthwhile writing the formulaf'(x)=h'(x)g(x)+h(x)g'(x)substitute into the formulatef'(x)=2x(x^1/2-7x)+(3+x^2)(1/2x^-1/2-7)
AS
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