Calculus

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Given F(2)=1,F'(2)=5,F(4)=3,F'(4)=7 and G(4)=2,G'(4)=6,G(3)=4,G'(3)=8, find:
a)H(4)if H(x)= F(G(x))
b)H'(4)if H(x)= F(G(x))
c)H(4)if H(x)= G(F(x))
d)H'(4)if H(x)= G(F(x))
e)H'4 if H(x)= F(x)/G(x)

Please Help!

  • Calculus -

    a) H(4) = F(G(4)) = F(2) = 1
    b) H'(4) = F'(G(4)) * G'(4) = F'(2) * 6 = 5*6 = 30
    c) H(4) = G(F(4)) = G(3) = 4
    d) H'(4) = G'(F(4)) * F(4) = G'(3) * 3 = 8*3 = 24
    e) H'(4) = (F'(4) G(4) - F(4) G'(4))/[G(4)]^2 = (7*2-3*6)/4 = -1

  • Calculus -

    Thank you

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