00:01
In this case, given question, in solution we will write, we have given that the function, equation as f of x comma y, which is equal to x a to the part of minus y plus five by.
00:23
So the concept over here is the partial derivation, partially derivation of function, function f of x comma y with respect to x will give us the slope in x direction in x direction and the partial differentiation of function f of x com of y with respect to y with respect to y through y will give us slope will give us slope with with y direction.
01:27
So this is our concept and now let's see our sentence first part of the question now.
01:32
So we will find here slow in x direction in x direction so that is for point 3 comma 0 is will be as d by d x of function of x comma y and that is equal to d by d x our function is x e to the power of minus y press 5 by so we will differentiate function with respect to x keeping y constant and that's why we will get here e to the power of minus y added by 0 so we put here x as equal to 3 and y as equal to 0 to find slope at 3 comma 0 so that the value will be equal to 3 to the power of minus 0 added by 0 will be equal to e to the power of 0.
02:34
And as per the rule of differentiation, we know that d by dx, f of x comma y, which is equal to 1 at the point 3 .0.
02:47
So here we have our solution for the first part which is for x direction.
02:52
Now let's move on to the second part of the question.
02:54
So for part b, we'll find our slope of function of x comma y in y direction, right point 3 .0.
03:14
So now when this finder slope, that will be as equal to y by d y of f of x .coma y and we will get here d on d y.
03:28
X e to the power of minus y added by 5.
03:33
So we will get here as x e to the part of minus y multiplied by minus 1 added by 5...