00:01
In this problem, we are asked to evaluate the partial derivatives of this function, minus 4e to the 2x minus 5 .5.
00:14
And then we are asked to evaluate these partial derivatives at certain points.
00:20
The first one is at the point 2 minus 1.
00:23
And the second one is the partial derivative with respect to y evaluate you at 3 and 2.
00:28
So when we're taking partial derivatives, whatever else variable there is, we're taking with respect to the derivative of, we just ignore those and treat those as numbers.
00:41
So when we're taking the partial derivative of f, which is this symbol with respect to x, we're just going to treat this y as if it's just a number.
00:56
And as you remember, when you're taking the derivative for an exponential, you first take the derivative of the exponent, and then you multiply that with the number out front, and then leave the exponential by like itself.
01:12
So this would tell us that this is going to be equal to minus 8 times e to the 2x minus 5y.
01:24
And if you put in the numbers...
01:30
This should be equal to minus 8 to the exponential of 9, which is actually quite a big number.
01:39
And it turns out to be 64 ,824 .67.
01:49
Now let's do it for df of df, df, dy, which is the partial derivative of f respect to y...