00:02
We want to find the derivative of f of x equals 8 times the square root of 1 plus square root x.
00:09
So we're going to be using calculus shortcuts to make solving this derivative easier than using the traditional definition.
00:15
So let's proceed to define these relevant shortcuts.
00:17
We have 1 through 3 here.
00:19
One, the power rule, ddxx to the a equals a x to a minus 1.
00:22
Two, the product rule, ddx fdx fdxg plus fdgdx.
00:26
And three, the chain rule, dv, f of g of x is f prime g of x times g prime of x, the derivative of what's inside.
00:32
We're going to rely on the chain rule combined with the power rule to solve this...