Asked by Mikey
Knowing that
F(-2) = -7, F'(-2)= 12, g(-2)= -3 and g'(-2)= -9,
Compute:
a) h'(-2) if h(x)= f(x)g(x)
b) h'(-2) if h(x) = f(x) / g(x)
c) h'(-2) if h(x) = g(x) / 1+(f(x))^2
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F(-2) = -7, F'(-2)= 12, g(-2)= -3 and g'(-2)= -9,
Compute:
a) h'(-2) if h(x)= f(x)g(x)
b) h'(-2) if h(x) = f(x) / g(x)
c) h'(-2) if h(x) = g(x) / 1+(f(x))^2
Show all steps
Answers
Answered by
Steve
just use the chain rule
(a) h' = f'g + fg' = (12)(-3)+(-7)(-9) = 27
(b) h' = (f'g-fg')/g^2 = ((12)(-3)-(-7)(-9))/(-3)^2 = -11
(c) h' = (g'(1+f^2))-g(2ff'))/(1+f^2)^2
= ((-9)(1+(-7)^2))-(-3)(2(-7)(12))/(1+(-7)^2)^2
= -281376/625
(a) h' = f'g + fg' = (12)(-3)+(-7)(-9) = 27
(b) h' = (f'g-fg')/g^2 = ((12)(-3)-(-7)(-9))/(-3)^2 = -11
(c) h' = (g'(1+f^2))-g(2ff'))/(1+f^2)^2
= ((-9)(1+(-7)^2))-(-3)(2(-7)(12))/(1+(-7)^2)^2
= -281376/625
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