00:01
Hi there.
00:03
In this problem, we're asked to find all three partial derivatives of this function.
00:08
So we'll begin with x.
00:11
Notice we have e to some function.
00:15
So we'll need the chain rule here.
00:17
So we'll start from the outside.
00:19
The derivative, as always, of e to anything, is itself, or e to that exponent.
00:26
Now the chain rule tells us we need to multiply by the derivative of that exponent.
00:31
Now by derivative, we mean the partial derivative with respect to x of that exponent.
00:38
Okay, so we will keep our e to the minus x, y, z there.
00:44
And the partial derivative of negative x, y, z with respect to x, remember, we're treating x, or we're treating y and z as constants.
00:54
We're treating x like the variable.
00:55
So the derivative of negative x, y, z with respect to x, is just negative y z.
01:02
We're using the power rule in x it goes from x to one so that's all we get so a final answer will be negative y z e to the minus x y z okay now partial with respect to y this will feel exactly the same once again we start from the outside so e to that inner function and this time we want to multiply by the derivative but it's the partial derivative with respect to y of that inner function that's the only thing that's different this time.
01:36
We can see what's going to happen...