Partial Derivatives: Examples

1. Find f_x and f_y for the following function at the point (1,ln(2)):  f(x,y)=x*exp(x^2*y).

Anwser:

To do this,  we use the diff comand then the eval command to put in the variables:

>	diff(x*exp(x^2*y),x);

>	eval(%,[x=1,y=ln(2)]);

>	diff(x*exp(x^2*y),y);

>	eval(%,[x=1,y=ln(2)]);

2.Find f_xx , f_{xy ,} f_yxand f_yy for the following function: f(x,y)=x^3*y^3+2*x^4*y^9.

Anwser

To do this, use the diff command:

>	diff(x^3*y^3+2*x^4*y^9,x,x);

>	diff(x^3*y^3+2*x^4*y^9,y,x);

>	diff(x^3*y^3+2*x^4*y^9,y,y);