Question

Which order of differentiation will calculate
f(x,y)
faster:
x
first or
y
first?
Try to answer without writing anything down.

f(x,y)=xsiny+e^y

Answer 1

@hartnn

Answer 2

what do u need to calculate ?

Answer 3

f'(x,y) ?

Answer 4

I saw this question in mixed partial derivatives section It's just asking fxy(x,y) would be faster or fyx(x,y)

Answer 5

\[\begin{align}
f(x,y) = x\sin(y)+e^y & \\
&: f_x(x,y) = \sin(y) +0 \\
&:f_{xy}(x,y) = \cos(y) \\ \\
&:f_y(x,y) = x\cos(y)+e^y \\
&:f_{yx}(x,y) = \cos(y) \\
\end{align}\]

This si Clairaut's Theorem, isn't it?

Answer 6

I would say \(x\) first.

Answer 7

me goin with y

Answer 8

@wio Is it just a random guess or is their a way to do it? I know how to solve it @jhanny

Answer 9

Well, \(at+b\) is much more simple than \(a\sin t+e^t\).