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## 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?

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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