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**Unformatted text preview: **L16 – The Chain Rule πx 2 f (x) = tan g (x) = √ x2 + 4x − 5 Thm – If f and g are both diﬀerentiable and F = f ◦ g = f ( g (x) ), then F is diﬀerentiable and F (x) = Or if y = f (u) and u = g (x) are diﬀerentiable functions, then 1 Find f (x) if f (x) = tan πx 2 . If G(x) = √ x2 + 4x − 5, ﬁnd G (x) . 2 The Power Rule combined with the Chain Rule — If n is any real number and u = g (x) is diﬀerentiable, then or If g (x) = −4 (1 − 2x2 ) 4
3 ﬁnd g (x) . 3 If f (x) = (1 − 2x)4 (x − 3)3 ﬁnd f (x) . 4 Find F (x) where F (x) = x2 − 1 x2 + 3 2 . 5 Find d x sin(x) e . dx d dx 1 + ex 1 − ex 2 d xe−2x dx 6 Find dx a dx If f (x) = 46x−cos(x) ﬁnd f (x) . If f (x) = 34 ﬁnd f (x) . x 7 Where does the graph of y = √ x2 have horizontal tangent lines? 3 − 2x 8 Find the derivative of f (x) = sec2 ( sin(4x) ) . 9 Find the equation of the tangent line to y = sin3 (x) cos(3x) at x = π . 2 10 Find the slope of the tangent line to f (x) = √ x2 + 3 2x + 1 at x = 4 . 11 ...

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