ok i know the answer is 4(x^2+3)^3(2x) but i don't understand where did the (2x) come from Why wouldn't it just be 4(x^2+3)^3 since the rule is d/dx X^n = nx^(n-1)
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Originally Posted by jkami ok i know the answer is 4(x^2+3)^3(2x) but i don't understand where did the (2x) come from Why wouldn't it just be 4(x^2+3)^3 since the rule is d/dx X^n = nx^(n-1) Your rule is correct but you must also use the chain rule since your function is a function of a function! Let's imagine that , and Then your function can be written And the chain rule says that
thx
Last edited by jkami; February 14th 2009 at 04:12 PM. Reason: ...
differentiate (x^3+9)^4 I got two answers from different sources answer1 = 12x^2(x^3+9)^3 answer2 = 12x^3(x^3+9)^3
The first is correct. The Chain Rule states, . The rule works because the rate of change of multiplies the rate of change of . Hence, we have
Originally Posted by jkami differentiate (x^3+9)^4 I got two answers from different sources answer1 = 12x^2(x^3+9)^3 answer2 = 12x^3(x^3+9)^3 Perhaps an unorthodox way of differentiating but,one ,does not have to do repeated substitutions is the following:
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