The derivative of 5x²+10x+7 with respect to x is ____
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We are going to learn how to find the derivative of 5x2. This may seem a bit intimidating at first glance, but this is one of those derivatives that we have a nice formula for, and that makes our job a whole lot easier! Notice that 5x2 is in the form axn, where a is a constant. Well, like we just said, we have a general formula for the derivative of axn that we can apply to 5x2, and that is as follows:
If f(x) = axn, then f ' (x) = n⋅ax(n-1)
That's not so bad! All we have to do is identify our a and our n, and then plug those values into the formula, and we have our derivative!
In the case of 5x2, we have that a = 5 and n = 2. Therefore, we plug these into the formula and simplify.
n⋅ax(n-1) = 2⋅5x(2-1) = 10x1 = 10x
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