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## Homework Statement

Let ##\phi## be defined as follows:

##\phi(t)=\frac{sint}{t}## if ##t \neq 0##

##\phi(t)=1## if ##t = 0##

prove it's derivable on ##\mathbb{R}##

now let f be:

##f(x,y)=\frac{cosx-cosy}{x-y}## if ##x \neq y##

##f(x,y)=-sinx ## in any other case

express f as a function of ##\phi## and show f is differentiable in ##\mathbb{R}^2##

## The Attempt at a Solution

i had no problems in showing ##\phi## is derivable, but i have some problems in the second part.

i thought to do a composition of functions:

##f(\phi(t),y)=\frac{cos*(\frac{sint}{t})-cosy}{sint-y}## if ##sin(t) \neq y##

##f(\phi(t),y)=-sin*sint## in any other case

which would clearly be differentiable.

still i'm not sure this is the right way of reasoning.

am i wrong?

thanks in advance!