$a)y=(3x^5+2)(x+1)-\cos 3x\\ y'=15x^4(x+1)+3x^5+2+3\sin 3x\\ =18x^5+15x^4+2+3\sin 3x\\ b)y=\dfrac{5x^3-3}{x+1}-\sin^2x+\dfrac{5}{3}\\ y'=\dfrac{15x^2(x+1)-5x^3+3}{(x+1)^2}-2\sin x\cos x\\ =\dfrac{10x^3+15x^2+3}{(x+1)^2}-2\sin x\cos x\\ c)y=\dfrac{1}{\sqrt{2x-1}}+\sin\sqrt{x+1}\\ y'=-\dfrac{1}{2x-1}.2.\dfrac{1}{2\sqrt{2x-1}}+\dfrac{\cos\sqrt{x+1}}{2\sqrt{x+1}}\\ =-\dfrac{1}{\sqrt{(2x-1)^3}}+\dfrac{\cos\sqrt{x+1}}{2\sqrt{x+1}}\\ d)y=(5x^2-3)^5+\tan x\\ y'=5(5x^2-3)^4.10x+\tan^2x+1\\ =50x(5x^2-3)^4+\tan^2x+1$
