Suppose f(π/3) = 4 and f '(π/3) = −5, and let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x). Find the following.g'(π/3) h'(π/3)

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17-03-2018
Mathematics

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Suppose f(π/3) = 4 and f '(π/3) = −5, and let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x). Find the following.g'(π/3) h'(π/3)

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dat16d dat16d · Answer 1 · 2018-03-17T01:31:55+01:00

dat16d dat16d

17-03-2018

Use product rule and quotient rule, respectively. g'(x)=f(x)cos(x)+f'(x)sin(x). Plugging in Pi/3, we get 4(1/2)+(-5)(sqrt(3)/2).
For h'(x), we use quotient rule to find that h'(x)= (f(x)*(-sin(x))-cos(x)*f'(x))/(f(x))^2.
So h'(pi/3)= (4(-sqrt(3)/2)-(1/2)(-5))/16.

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