This video from IntegralCALC shows you how to solve the Product Rule f(x)=x(25-x) Math problem.
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Product Rule f(x) = x(25-x) Hi everybody! One more product rule problem tonight, it’s another basic one. It’s just f(x) = x(25-x). So, to take the derivative, we got f1(x)=—so, product rule again, taking the derivative of one term. In this problem, the terms are x and 25–x. So, we take the derivative of one term while we hold the other one constant and then we flip that. We’re going to go ahead and take the derivative of x, the first term here, the derivative of x is just 1, so that’s implied and then we’re going to write the second term because that stays the same and then we’re adding together. So, the 1, the derivative from the x is right there 25–x. Then this time, we flip it. We take the derivative of this and we got this the same. Now, we’re going to take the derivative of this and leave this the same. So, leaving x the same and we just write that and then the derivative of 25–x which is just -1, the derivative of 25 is zero, that goes away and the derivative of –x her is just -1. Now that we have that, we can simplify. We have 25 – x and then x×-1 here is a –x, so we can just say -x. So, the final answer is 25–2x. There you have it.
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