Find h'(2), given that f(2)= -3, g(2)= 4, f'(2)= -2, and g'(2)= 7
a) h(x)= 5f(x) - 4g(x)
b) h(x)= f(x)g(x)
c) h(x)= f(x)/g(x)
d) h(x)= g(x)/1 + f(x)
I have no idea how to plug these in. If someone could please show me how to go about one, I'm sure the rest would be nearly the same.
I'll do (c):
h(x)=f(x)/g(x)
use quotient rule in differentiation:
d(u/v)=(v*du-udv)/v²
so
h'(2)=(g(x)*f'(x)-f(x)*g'(x))/g(x)²
=(g(2)*f'(2)-f(2)*g'(2))/g(2)²
=(4*(-2)-(-3)*7)/4²
=13/16
Check my work.