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2311lectureoutline3.4

# 2311lectureoutline3.4 - 2 x Notice that in a composite...

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MAC2311, Calculus I 3.4 The Chain Rule – Finding Derivatives of Composite Functions The Chain Rule: If g is differentiable at x and f is differentiable at g(x) , then the composite function F = f g defined by F(x) = f(g(x)) is differentiable at x and F is given by the product ( ) ( ) ( ) ( ) F x f g x g x = . Here are a few example using the Chain Rule: Example 1: y = sin(3x 4 ) y’ = cos(3x 4 ) (12x 3 ) = 12x 3 cos(3x 4 ) Example 2: y = (5x 2 + 10x) 5 y’ = 5(5x 2 + 10x) 4 (10x + 10) Example 3: y = e tanx y’ = e tanx (sec
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Unformatted text preview: 2 x) Notice that in a composite function, you have an “outer” function and an “inner” function. So to differentiate a composite function, take the derivative of the outer function and multiply the result by the derivative of the inner function. The Chain Rule combined with the Power Rule: Let u be some function of x. If y = u n , then y’ = nu n-1 u’ The Derivative of an Exponential Function of any base: ln x x d a a a dx & ± = ² ³ Try exercises 10, 12, 14, 16, 22, 24, 30, 42, 50, 52 on pages 203-204 in your text....
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