00:01
In this problem, we have been asked to determine, d .d .x by implicit differentiation.
00:08
We have been given that x, sine, y, plus y, sine x, this is equal to 5.
00:16
So we want to use implicit differentiation.
00:18
We're going to differentiate both sides of this equation with respect to x.
00:22
First of all, we have the derivative of this, using the product rule of derivatives.
00:27
This is equal to the derivative of x times sine y, plus x times the derivative of sine y.
00:33
The derivative of sine is cost, so we have cost y, and using the chain rule with this, we need to multiply with the derivative of the argument y.
00:40
So we have d, y, d .x.
00:43
Now along with this, we add the derivative of this, using the product rule...