Evaluate the first partial derivative at the given point (1,2)

Question

Find the first partial derivatives of the function: x/y at the given point (1,2)

Answer 1

Auburn,

 

  When you take partial derivatives with respect to one variable, treat the others as if they were constants.

 

We are given f(x,y) = x/y and we are to find the partial derivatives. 

 

Since there are two variables, we take two partial derivatives: one with respect to x, the other with respect to y.

 

 

f_x(x,y) = (∂/∂x)(x/y) = 1/y

 

f_y(x,y)= (∂/∂y)(x/y) = -x/y²

 

 

Now just substitute to get the values of the partial derivatives at (1,2).

 

 

Geaux Tigers!