Let f ( x ) {\displaystyle \displaystyle f(x)} be a differentiable function, and suppose it is given that f ′ ( 0 ) = 10 {\displaystyle \displaystyle f'(0)=10} . Let g ( s , t ) = f ( a s − b t ) {\displaystyle \displaystyle g(s,t)=f(as-bt)} , where a {\displaystyle \displaystyle a} and b {\displaystyle \displaystyle b} are constants. Evaluate ∂ g ∂ s {\displaystyle \displaystyle {\frac {\partial g}{\partial s}}} at the point ( s , t ) = ( b , a ) {\displaystyle \displaystyle (s,t)=(b,a)} , that is, find ∂ g ∂ s | ( b , a ) {\displaystyle \displaystyle {\frac {\partial g}{\partial s}}{\bigg |}_{(b,a)}} .
be a differentiable function, and suppose it is given that 
. Let 
, where 
and 
are constants. Evaluate 
at the point 
, that is, find 
.
