Differentiate sin(2x+y)

[Bobby Bones]

The question is:
d sin(2x+y)
dx

How do I do this? The y in the equation is confusing me.

I used the chain rule and got (dy/dx) = 2cos(2x+y)

Is this correct?

 

[HallsofIvy]

You are NOT asked to find "$\displaystyle \frac{dy}{dx}$" because y is not a function of x! You are given f(x,y)= sin(2x+ y) where x and y are independent variables. The partial derivative with respect to x is, as you say $\displaystyle \frac{\partial f}{\partial x}= 2 cos(2x+ y)$ since when differentiating with respect to x, the independent variable, y, is treated as a constant.

(If you are told that y is a function of x rather than an independent variable, then the derivative is $\displaystyle cos(2x+ y)\left(2+ \frac{dy}{dx}\right)$.)

 

[Bobby Bones]

Thank you.