Thread: Backwards derivative problem

Before, I posted a problem about partial derivatives. Well, this time I have to use the partial derivative to find F(x,y), and I'm not really sure how to go about it. I am given the two following partial derivatives.

(1) The derivative of F with respect to x is x^2 divided by y

and

(2) The derivative of F with respect to x is xe^xy

Originally Posted by clockingly

Before, I posted a problem about partial derivatives. Well, this time I have to use the partial derivative to find F(x,y), and I'm not really sure how to go about it. I am given the two following partial derivatives.

(1) The derivative of F with respect to x is x^2 divided by y

and

(2) The derivative of F with respect to x is xe^xy

the same principle holds. integrate both with respect to x by treating y as a constant

Originally Posted by clockingly

(1) The derivative of F with respect to x is x^2 divided by y

Let f(x)=y.

That means,
y'=x^2/y

Thus,
y'*y=x^2

Thus,

INT y*y' dx = INT x^2 dx +C (Substitution rule is used implicity).

(1/2)y^2 = (1/3)x^3 +C

Okay, but which part is the F(x,y)?

Originally Posted by clockingly

Okay, but which part is the F(x,y)?

for the first one
F(x,y) = (x^3)/3y differentiate this to check it