If f(x)=sqrt (x^2-4) and g(x)=3x-2, then the derivative of f(g(x)) at x=3 is

A. 7/sqrt 5
B. 14/sqrt 5
C. 18/sqrt 5
D. 15/sqrt 21
E. 30/sqrt 21

1 answer

df/dx = df/dg * dg/dx
= g/√(g^2-4) * (3)
= 3(3x-2)/√((3x-2)^2-4)
= 3(3x-2)/√(9x^2-12x)

at x=3, that's

3(7)/√45
= 21 / 3√5
= 7/√5