Follow the proof of Theorem 2.6 in the text book( using the limit approach) to prove that: d d x [ cos x ] = − sin x 2.(a) Find the derivative of the function g ( x ) = sin 2 x + cos 2 x (b) then use a trigonometric identity to confirm the result in the quicker way. 3. Use implicit differentiation to prove that d d x [ x n ] = n x n − 1 4. A man 6 ft tall walks at a rate of 5 feet per second away from a light that is 15 ft above the ground. When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving?
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