Answer to Question #101363 in Calculus for nimra

Question

f(x)=3x+3y+sinxy+cosy

Answer 1

The given equation,

$f(x)=3x+3y+sinxy+cosy$

Differentiating this equation with respect to x gives,

$f'(x)=3+ycos(xy)$

Also by integrate the given equation with respect to x,

$\int(3 x + 3 y + sin(x y) + cos(y)) dx \\=\frac{3}{2}x (x + 2 y) + x cos(y) - cos(x y)/y + constant$