My calc professor offered 20 points extra credit on the final to anyone that could differentiate a chain rule problem, using the derivative. (His example was xe^x). I consider myself pretty good at math, but after an hour of trying I just can't get it.
So could anyone show the steps to differentiate xe^x using the definition of the derivative (f(x+h)-f(x))/h
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Well since you have to do it by the definition the teacher is really just testing your algebra skills. I am assuming that you know what the definiton of the derivative is. If you do just solve the limit.
This kids right. To do the derivative of xe^x you use the product rule which is the derivative of u times v plus the derivative of v times u. u is x and v is e^x. So the derivative of x is 1 so the first term is e^x then the derivative of e^x is just e^x. so the second term is xe^x. so you get e^x + xe^x. And this isn't a chain rule problem it's a product rule problem. You could probably find that using the definition of the derivative, but that's why more work and impossible to explain online
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