A.
[tex]y=\sin(x^2+3x-1)[/tex]
[tex]\implies y'=\cos(x^2+3x-1)(x^2+3x-1)'=(2x+3)\cos(x^2+3x-1)[/tex]
B.
[tex]y=x^3+\sin x[/tex]
[tex]\implies y'=3x^2+\cos x[/tex]
[tex]\implies y''=6x-\sin x[/tex]
[tex]\implies y'''=6-\cos x[/tex]
C.
[tex]y=\left(x+\dfrac1x\right)^2[/tex]
[tex]\implies y'=2\left(x+\dfrac1x\right)\left(x+\dfrac1x\right)'=2\left(x+\dfrac1x\right)\left(1-\dfrac1{x^2}\right)=2\left(x-\dfrac1{x^3}\right)[/tex]
D.
[tex]y=(5x-2)^{-2}[/tex]
[tex]\implies y'=-2(5x-2)^{-3}(5x-2)'=-10(5x-2)^{-3}=\dfrac{10}{(2-5x)^3}[/tex]
