Question

z=sin(xy)+(cos(xy))^2用全微分四则运算法则求全微分

Answer 1

问：z=sin(xy)+(cos(xy))^2用全微分四则运算法则求全微分

答：亲亲~您好，很高兴为您解答哈~。z=sin(xy)+(cos(xy))^2用全微分四则运算法则求全微分如下：设z=f(x,y)=sin(xy)+(cos(xy))^2，则有：∂f/∂x = y*cos(xy) - 2*y*sin(xy)*cos(xy)，∂f/∂y = x*cos(xy) - 2*x*sin(xy)*cos(xy)，根据全微分四则运算法则，全微分dz可表示为：dz = ∂f/∂x * dx + ∂f/∂y * dy，将∂f/∂x 和∂f/∂y 的表达式代入上式，得到：dz = (y*cos(xy) - 2*y*sin(xy)*cos(xy)) * dx + (x*cos(xy) - 2*x*sin(xy)*cos(xy)) * dy，因此，z=sin(xy)+(cos(xy))^2的全微分为：dz = (y*cos(xy) - 2*y*sin(xy)*cos(xy)) * dx + (x*cos(xy) - 2*x*sin(xy)*cos(xy)) * dy。