So I have this function $f(x,y,z)=x\sin(y-z).$
And I want to find :
the derivative with respect to $x$
the derivative with respect to $y$
the derivative with respect to $z .$
I think I should use the multivariable chain rule, but since I have dyscalculia I am not sure how to proceed adeguately .
I know that for the two variable chain rule,
$$\text{if} \quad f(x)=h(g(x)) \quad \text{then}\quad f'=h'(g(x))\cdot g'(x).$$ This formula for me is clear and I understand it well enough.
I have seen some formulas with three variables and they all seem very confusing for me so my question is,
could you please help me with a formula to find the derivative of a function composed of three variables with the same terms that i used in the equation above? meaning a formula with $h,g,$ possibly and variable, maybe $i?$ Possibly followed with partial derivatives formula related to a $3$ variable composite function
It would be really important for me if the formula could be in the same style of
$f(x)=h(g(x))$ then $f'=h'(g(x))·g'(x).\;$ (so a formula for composite function )
Thanks !!