Question

How do you find the partial derivative of `f(x,y) = sin 3x + cos 5y`?

Answer 1

Hey there :)

Here's the answer with no taste.

`f_x(x, y) = 3cos(3x)` and `f_y(x, y) = -5sin(5y)`

Now the juicy parts.

To find `f_x(x, y)`, fix all other variables as constants, in this case just `y`.

So for `f_x(x, y)` we know that `cos(5y)` is only a function of `y` so we differentiate it like a constant since `y` is fixed. So we just differentiate `sin(3x)` in terms of `x` yielding `3cos(3x)`.

This is

`f_x(x, y) = 3cos(3x)`

Similarly, for `f_y(x, y)`, we hold `x` fixed and differentiate with respect to `y` to get

This is

`f_y(x, y) = -5sin(5y)`