fx y x2 sinxySolution The answer will be 35 times the parti

f(x, y) = x2 sin(xy)

Solution

The answer will be 3/5 times the partial derivative of f with respect to x, minus 4/5 times the partial derivative of f with respect to y, evaluated at the point x=1, y=pi. OK. So, the partial derivative of f w/r/t x is (2x)sin(xy) + (x^2)y*cos(xy). At (1,pi), this is 0 + pi*(-1). The partial derivative of f w/r/t y is (x^3)cos(xy). At (1,pi), this is (1)*(-1). So the directional derivative along the direction given by the unit vector is - (3pi + 4)/5.