Maths calculus?

Question

If I multiply out (x-5) squared I get x squared -10x +25 as my answer. However, The Chain Rule gives me 2(X-5) to the power of 1. Am I confusing things? I thought The Chain Rule saved multiplying out many powers.

Answer

You need to back up and learn what the words mean. You are jumbling things together that do not belong together. There is no "chain rule" in multiplying. 

The first derivative of (2x - 5)^2 is 2(x - 5)dx.
The first derivative of x^2 - 10x + 25 is (2x - 10)dx.
Same either way.

Answer

f(x) = (x - 5)&sup2; = x&sup2; - 10x + 25
f'(x) = 2x - 10

f(g(x)) = (x - 5)&sup2; with g(x) = (x - 5) and f(x) = (g(x))&sup2;. Thus
f'(x) = 2g(x) * g'(x)
g'(x) = 1
f'(x) = 2(x - 5) * 1 = 2x - 10

There is not only one way to achieve your objectives, even in maths.

Maths calculus?

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