00:01
We are as to assume that xy is equal to 2 and it is given that the value of d .y by dt is equal to 5 and we need to find the value of d x by dt when x is equal to 5 understand that if we differentiate the given equation with respect to the variable t we can find the value of d x by d t so let's differentiate the given equation with respect to the variable.
00:37
To differentiate the left hand side of the equation, we need to use the product rule.
00:42
So first we need to keep x as it is and we need to differentiate y with respect to the variable t.
00:48
So we will have dy by dt plus we need to keep y as it is and we need to differentiate x with respect to the variable t.
00:59
If we do that we will have dx by dt.
01:02
And on the right hand side if we differentiate 2 with respect to the variable t we will get 0.
01:09
Now what we want is the value of d x by d t that is right here and we know the value of d .y by dt it is given as 5 and the value of x is equal to 5 but we don't know the value of y.
01:26
To find the value of y we can use the given equation.
01:29
It says that x times y is equal to 2 we know the value of x so we can substitute the value of x in the given equation so we will have 5 times y is equal to 2 so the value of y will be equal to 2 divided by 5 when x is equal to 5 if we multiply these two expressions we will get 2 so the value of y is what we have here so from this we can find the value of d x by d t now let's keep the term that has dx by dt on the left hand side and let's shift all other terms to the right hand side of the equation.
02:10
So we will have y times dx by dt on the left hand side and on the right hand side we will have minus x times d .y by dt...