00:01
Let's start by integrating the function h.
00:04
So to find h prime of x we need to use the quotient rule.
00:10
The quotient rule says that the derivative is equal to the denominator which is f of x times cosine x times the derivative of the numerator which is 3e to the x power plus g prime of x minus the numerator 3e to the x power plus g of x times the derivative of the denominator.
00:36
For that i will use the product rule.
00:40
So we have f of x times the derivative of cosine which is negative sine x plus the derivative of f which is f prime of x times cosine of x.
00:54
So this is multiplied here and we divide all of this by the denominator squared.
01:05
So f of x squared times cosine squared x.
01:12
And we want to evaluate this when x is zero.
01:16
So h prime of zero is f of zero times cosine of zero times the derivative of the numerator multiplied by 3 times e to the zero with power.
01:28
E to the zero with power is just one.
01:31
Okay and then we have g prime of zero minus 3 times e to the zero with power which is just 3 plus g of zero and we multiply by negative f of zero times sine of zero...