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a)
D\sin x=\cos x
b)
D\ 5\sin x+\pi=5\cos x
c)
D\ 2x+7\cos x=-7\sin x+2
d)
D\ x^4-5x^3-4\cos x=4x^3-15x^2+4\sin x
e)
D\ \frac{\sin x}{3}=\frac{3\cos x-9\sin x}{9}
f)
D\ \frac{\sin x-2\cos x}{2}
f\left(x\right)=\sin x-2\cos x
f'\left(x\right)=\cos x+2\sin x
g\left(x\right)=2
g'\left(x\right)=0
D\ \frac{f\left(x\right)}{g\left(x\right)}=\frac{f'\left(x\right)g\left(x\right)-f\left(x\right)g'\left(x\right)}{\left(g\left(x\right)\right)^2}=\frac{2\left(\cos x+2\sin x\right)\cdot0\left(\cos x+2\sin x\right)}{4}=\frac{2\cos x+4\sin x}{4}
=\frac{\cos x+2\sin x}{2}