00:01
So we have this function, y is equal to e to the power of x, multiplied by cosine of x, and we're going to find a tangent line to this function at x is equal to zero.
00:09
So let's first figure out what our y value is when x is equal to zero.
00:12
So we're going to have y is equal to e to the zero times cosine of zero, which is equal to one times one, which is just one.
00:20
So the point that we're looking at is zero comma one, and that'll come in handy later.
00:26
Let's now look at what our derivative function, is going to be.
00:31
So we're going to use the power rule here, which is the derivative of the first term.
00:36
And the reason we're using the power rule is because we have two terms multiplied together where the x is are kind of in different places.
00:42
So we can't just take a regular derivative.
00:45
We actually have to use the power rule here.
00:47
So we have e to the x, which is the derivative of that is e to the x multiplied by the second term, which is just cosine of x...