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Calculus

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Suppose f(pi/3) = 3 and f '(pi/3) = −7,
and let g(x) = f(x) sin x and
h(x) = (cos x)/f(x). Find the following.

a. g'(pi/3)


b. h'(pi/3)

  • Calculus - ,

    g = f*sin(x)
    g' = f'*sin(x) + f*cos(x)
    g'(pi/3) = (-7)*√3/2 + 3*1/2 = (3-7√3)/2



    h = cos(x)/f
    h' = (-sin(x)*f - cos(x)*f')/f^2
    h'(pi/3) = [(-√3/2)*3 - (1/2)(-7)]/9 = (7-3√3)/18

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