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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

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1 answer

  1. 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

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