00:01
So in this problem we're given xy plus 8 e to the y equals 8 e and we're asked to find y prime prime when x is 0.
00:07
First off when x is 0 we need to find out what y is because we need to plug it in later.
00:12
So we plug in 0 for x in this equation.
00:16
First term goes away leaving us with 8 e to the y equals 8 e so y so y would be equal to 1.
00:22
And then we take the derivative of the equation.
00:24
The first term is a product rule.
00:26
So we have x times the derivative of y plus y times the derivative.
00:30
Of x, which is just one.
00:32
And then the next term, the derivative of an exponential is an exponential.
00:35
So we'll have 8e to the y, but we make sure to multiply by the derivative of the exponent because of the chain rule.
00:41
And that equals zero, the derivative of 8e...