If y=A sin(wt-kx),then the value of dy/dx is. Please explain this question in detail.

Dear student 
 y = A sin(wt-kx)
Then, dy/dx = A cos(wt -kx) *  d/dx(-kx)
dy/dx =  -Ak cos(wt - kx)
So, D is correct option .
Hope this helps 
Regard