Ge 207c 1 cos x x sin x hung nguyen f x x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ྎ − 1 ⎞ྏ x −4 / 3 ⎜ྎ ⎟ྏ dx dx ⎝ྎ 3 ⎠ྏ 1 f ' ( x) = 3x 2 sin( x) + x 3 cos( x) − x − 4 / 3 3 f ( x) = ) 1− x 2% d" 1 − x '(1 − x ) − 1 − x $ # & f '( x ) = dx 2 (1 − x ) = sin x c. GE 207C 1 + cos x x + sin x Hung Nguyen f (x) = ( x + sin x ) ( x + sin x ) d d (1 + cos x ) − (1 + cos x ) ( x + sin x ) dx dx 2 ( x + sin x ) d d (− sin x ) − (1 + cos x ) (1 + cos x ) dx dx 2 ( x + sin x ) = − ( x + sin x ) sin x − (1 + 2 cos x + cos2 x ) = − ( x sin x + sin x ) − (1 + 2 cos x + cos x ) ( x + sin x ) = = = 2 2 = 2. In the figure 2 ( x + sin x ) 2 ( x + sin x ) 2 − x sin x − (sin 2 x + cos2 x ) − 1 − 2 cos x ( x + sin x ) 2 − x sin x − 1 − 1 − 2 cos x ( x + sin x ) 2 − x sin x − 2 − 2 cos x ( x + sin x ) 2 =− x sin x + 2 + 2 cos x ( x + sin x ) 2 f ( x ) = 10 sin () x − 6 x cos The semi- circle and the parabola have common tangents at two values of x. If the semi- circle and the parabola are the respective graphs of x () find the value of b. h. − x sin x − sin 2 x − 1 − 2 cos x − cos2 x g. GE 207C 1 + cos x x + sin x f '( x ) = = Problem Set 06 Solution 3.3 Derivatives of Trigonometric Functions 3.4 Chain Rule f ( x ) = 4 sin x + 5 csc x 2 Hung Nguyen 3. Determine f f ( x) = (...
View Full Document

Ask a homework question - tutors are online