00:01
In this question, we are asked to calculate dz over dt at t equals 0.
00:05
First note that z is a function of x and y and each of x and y are functions of t.
00:13
So to calculate, to find the formula for dz over dt we'll use the chain rule.
00:18
By the chain rule, we'll get dz over dx multiplied by dx over dt plus dz over dy multiplied by dy over dt.
00:34
Now we need first to calculate dz over dx and dz over dy.
00:40
Dz over dx equals d over dx of x cubed y squared plus xy to the fourth.
00:51
This equals 3x squared y squared plus y to the fourth.
00:59
Let's calculate dz over dy.
01:04
That's d over dy of x cubed y squared plus xy to the fourth.
01:14
We'll get 2x cubed y plus 4xy cubed.
01:24
Now we need to calculate dx over dt and dy over dt.
01:32
X equals sine t, therefore dx over dt equals cosine t.
01:38
And since y equals e to the t, dy over dt equals e to the t...