Differential Functions
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Assume that f/g (x) = x^2 + 2x, where f and g are differentiable functions such that f(2) = 2 and f'(2)= 3. Find g'(2).
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f/g(x) = x^2 + 2x.....
or g(x) = f(x)/ (x^2 + 2x) or f(x)*(x^2 + 2x)^-1
g'(x) = f(x)*-1(x^2 + 2x)^-2*(2x+ 2) + f'(x)*(x^2 + 2x)^-1
therefore g'(2)= f(2)*-1(2^2 + 2*2)^-2*(2*2+ 2) + f'(2)*(2^2 + 2*2)^-1
= -2*((8)^-2)*6 + 3*((8)^-1)
= -12/64 + 3/8
= 12/64 or 3/16.
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