If y = exp(x^2), find dy/dx
Recall that the derivative of exp(x) is exp(x), but notice this question is slightly more complex due to the x^2 term. This is example of differentiationg composite functions, and so the chain rule is required. To begin, we'll set u = x^2, and then compute du/dx = 2x. Furthermore, we observe that y = exp(u) and dy/du = exp(u). Then, by the chain rule, we have dy/dx = dy/du * du/dx = exp(u) * 2x = exp(x^2) * 2x.
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