The given function is of the form U 4 where U = x 3 + 4. One of them is to consider function f as the product of function U = sqrt x and V = (2x - 1)(x 3 - x) and also consider V as the product of (2x - 1) and (x 3 - x) and apply the product rule to f and V as followsĮxpand and group like terms to obtain the derivative f'.Įxample 7: Find the derivative of function f given by There are several ways to find the derivative of function f given above. We use the product rule for f and the quotient rule for V as followsĮxpand and group to obtain the derivative f'. Write all terms in the numerator so that they have the same denominator 2 sqrt xĮxpand and group like terms to obtain f'(x)Įxample 5: Calculate the first derivative of function f given byįunction f given above may be considered as the product of functions U = 1/x - 3 and V = (x 2 + 3)/(2x - 1), and function V may be considered as the quotient of two functions x 2 + 3 and 2x - 1. The given function may be considered as the ratio of two functions: U = x 2 + 1 and V = 5x - 3 and use the quotient rule to differentiate f is used as followsĮxpand and group to obtain f'(x) as followsĮxample 4: Calculate the first derivative of function f given byįunction f is the quotient of two functions hence the use of the quotient rule
F'(x) = \dfracĮxample 3: Calculate the first derivative of function f given by
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