Use limits to find f' (x) if f(x) = 7x.

Question

Accepted Answer

Welcome back, everyone. Determine the derivative of the function G of X equals 5x using the limit definition of the derivative. We're given 4 answer choices A says 0, B5, C 10, and D1. So let's recall that the derivative of G of X, specifically G of X, can be evaluated using limits, and we get limit as H approaches 0. And then we're looking at G at point X plus H minus G of X divided by H. All that we have to do is simply evaluate the G of X plus H. So we get limit as H approaches 0 of 5 in C X plus H. we are subtracting G of X itself, which is 5 X, and we're dividing the result by H. So now let's distribute the terms we're going to get. 5 x plus 5 h in the numerator we're subtracting 5 x and dividing by H. Now we can notice that 5 x and -5 X, those can be canceled out and we end up with limit. As H approaches 0 of 5 H divided by H, those can be canceled out as well. We can cancel out the H and we simply get the limit of 5. Notice that it's independent of H and the limit of a constant is the constant itself, so it is equal to 5, meaning the final answer to this problem corresponds to the answer choice B. Thank you for watching.

Use limits to find f' (x) if f(x) = 7x.

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