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Question
I am prepping for ACTs, working on the Chain Rule. The question in my workbook I'm having trouble with is:

If f(x)=(x+5)^10, find f'(x)

Thanks,
John

Answer
You simply have to bring forward the index value of 10, and subsequently reduce it by 1:

f'(x)= 10 (x+5)^9   (shown)

Do note though you have to differentiate x+5 wrt x as well (although it gives you the implicit value of 1.)

So if I modify the problem as f(x)=(2x+5)^10,

then f'(x) = 10 (2x+5)^9 * (2)       (differentiating 2x+5 wrt x gives the value of 2)

         =  20 (2x+5)^9 (shown)

Hope this clarifies. Peace.

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