SOLUTION: Use the product rule with g = f to show that if f is differentiable, then d/dx[f(x)]^2 = 2f(x)f'(x)

SOLUTION: Use the product rule with g = f to show that if f is differentiable, then d/dx[f(x)]^2 = 2f(x)f'(x)

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Question 408579: Use the product rule with g = f to show that if f is differentiable, then
d/dx[f(x)]^2 = 2f(x)f'(x)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Since f(x)^2 = f(x)f(x), we can take the derivative using the Product rule to obtain:

d/dx [f(x)f(x)] = f'(x)f(x) + f(x)f'(x) = 2f(x)f'(x).
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