question archive If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x)
If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x)
Subject:MathPrice:2.85 Bought3
If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). Find u'(1) Find v'(5).
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
u(x) = f(x) g(x)
u'(x) = f'(x) g(x) + f(x) g'(x)
u'(1) = f'(1) g(1) + f(1) g'(1) = 2 * 1 + 2 * (-1) = 2 - 2 = 0
v(x) = f(x) / g(x)
v'(x) = ( g(x) f'(x) - f(x) g'(x) ) / g^2 (x)
v'(5) = ( g(5) f'(5) - f(5) g'(5) ) / g^2 (5) = ( 2*(-1/3) - 3*(2/3) ) / 2^2 = (-8/3) / 4 = -2/3
