Question Number 226821 by Spillover last updated on 16/Dec/25
$${Differentiate}\:\: \\ $$$$\mathrm{20sin}\:\left({x}+\mathrm{3}\right)\mathrm{cos}\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$
Answered by AgniMath last updated on 16/Dec/25
![(d/dx) sin(x+3) = cos(x+3) (d/dx) cos(x^2 /2) =−xsin(x^2 /2) (d/dx) 20sin(x+3)cos(x^2 /2) = 20[cos(x+3).cos(x^2 /2)+sin(x+3).(−xsin(x^2 /2))] = 20(cos(x+3)cos(x^2 /2)−xsin(x+3)sin(x^2 /2))](https://www.tinkutara.com/question/Q226824.png)
$$\frac{{d}}{{dx}}\:{sin}\left({x}+\mathrm{3}\right)\:=\:{cos}\left({x}+\mathrm{3}\right) \\ $$$$\frac{{d}}{{dx}}\:{cos}\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:=−{xsin}\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\frac{{d}}{{dx}}\:\mathrm{20}{sin}\left({x}+\mathrm{3}\right){cos}\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$=\:\mathrm{20}\left[{cos}\left({x}+\mathrm{3}\right).{cos}\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{sin}\left({x}+\mathrm{3}\right).\left(−{xsin}\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right)\right] \\ $$$$=\:\mathrm{20}\left({cos}\left({x}+\mathrm{3}\right){cos}\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−{xsin}\left({x}+\mathrm{3}\right){sin}\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right) \\ $$
Commented by Spillover last updated on 16/Dec/25
$${thanks} \\ $$