Calculus Section 3.6 Use the Chain Rule to differentiate functions

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Presentation transcript:

Calculus Section 3.6 Use the Chain Rule to differentiate functions A composite function is formed by the composition of two functions. Consider: h(x) = x3 and g(x) = 4x + 2, their composition is: h(g(x)) = (4x+2)3 The Chain Rule is used to find the derivative of a composite function. Chain Rule If f(x) = h(g(x)), then f’(x) = h’(g(x))∙ g’(x)

Use the Chain Rule to differentiate. f(x) = (4x+2)3 y = (7x2 + 5x – 2)4

Find the derivative f(x) = y =

Find the slope of the function when x = 1. f(x) = f(x) = (2x-5)(5x – 6)3/2

Find the instantaneous rate of change when x = 2. y =

assignment Page 151 Problems 2 – 46 even