Y Sin2X. = 4(1+ cos 2x) sin2x Example 2 y = sin (cos (x 2)) y‘ = cos(cos (x 2)) sin (x 2)) 2x = 2x sin (x 2) cos (cos x 2) Note We do not need to remember the chain rule formula Instead we can just apply the derivative formulas (which are in terms of x) and then multiply the result by the derivative of the expression that is replacing x For example d/dx ( (x 2 + 1) 3) = 3 (x 2 + 1) 2.
Diagram Of Mathematics Function Y Sin 2x Stock Vector Vector And Low Budget Royalty Free Image Pic Esy 017699073 Agefotostock from agefotostock.com
Example 2 Find the integral of x sin2x by using integration by parts formula Solution To find the integration of the given expression we use the integration by parts formula ∫ uvdx = u∫ vdx ∫( u’ ∫ vdx)dx Here u = x and v = Sin2x ∫x sin2x dx =x∫sin2xdx d/dx x∫ sin2xdx dx =x cos2x/2 ∫(1cos2x/2) dx =cos2x/2 dx + 1/2 cos2xdx =xcos2x/2 + sin2x/4 + C.
