The chain rule

 $y\ =\ \sin x$  Differentiate this function.

•  $\cos x\$  

•  $-\cos x$  

•  $\tan x$  

• none of the above

 $y\ =\ \cos x$  Differentiate this function.

•  $\sin x$  

•  $-\sin x$  

•  $\tan x$  

• None of the above

 $y=4\cos x$  Differentiate

•  $y=4\sin x$  

•  $y=-4\sin x$  

• None of the above

 $y\ =3x\ +2\sin x$  Differentiate

•  $3+2\cos x$  

•  $3-\cos x$  

•  $3-2\cos x$  

 $y=\left(2x^2+3x+4\right)^{\frac{1}{2}}$  Differentiate using the chain rule

•  $y\ =\frac{4x+3}{2\left(2x^2+3x+4\right)^{\frac{1}{2}}}$  

•  $y=2x\left(2x^{2\ }+3x\ +4\right)^{\frac{-1}{2}}$  

 $y=\left(1+\sin x\right)^3$  Differentiate

•  $3\cos x\left(1+\sin x\right)^2$  

•  $3\left(1+\sin x\right)^2$  

 $y\ =\sin\left(3x^2+4\right)$  Differentiate

•  $\cos\left(3x^{2\ }+4\right)$  
  

•  $\ 6x\cos\left(3x^2\ +4\right)$  
  

 $y=\left(\sin2x\right)^2$  differentiate

•  $2\left(\sin2x\right)^{ }$  

•  $2\cos2x\sin2x$  or  $2\sin2x\cos2x$  

 $y\ =\ 12x^{\frac{2}{3}}$  differentiate

•  $\frac{4}{3}x^{\frac{-1}{3}}$  

•  $8x^{\frac{-1}{3}}$  

•  $\frac{2}{3}x^{\frac{-1}{3}}$  

 $y=\sqrt{x}\left(x+1\right)$  Differentiate

•  $\frac{dy}{dx\ }=\frac{3}{2}x^{\frac{1}{2}}+\frac{1}{2\ }x^{\frac{-1}{2}}$  

•  $\frac{dy}{dx}=\ x^{\frac{3}{2}}+x^{\frac{1}{2}}$  

•  $\frac{dy}{dx}=\ \frac{1}{2\ }x^{\frac{1}{2}}\ -\frac{1}{2\ }x^{\frac{-1}{2}}$