2x sec(x²)     

  2sec(x²)      

  4xsec²(x²)

$\frac{\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}$

$\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(1+x^2\right)}}$

$\frac{x\sec^2\left(x^2+1\right)}{\sqrt{\tan\left(x^2\right)}}$

Cosx²e^x3 cos(e^x3)     

   cos3x² e^x2 cos(e^x2)     

 cos2xe^x2 cos (e^x2)

2xcos(x²)        

 sinsin(tanx)x      

 -sinsin(tanx)x

2cos2x     

  2 sinx       

 cos2x

Cosx²e^x3 cos(e^x3)   

cos 3x² e^x3 cos( e^x3)   

  -(4x-6)cos cos (2x²-6x)          

F’[g(x)] 

  f’[g(x)]g’(x)           

   f’[g(x)]g(x)

$\frac{dy}{du}$

$\frac{dy}{dx}\ \frac{dx}{du}$

$\frac{dy}{du}\ \frac{du}{dx}$

2xcos(x²) 

  2cos(x²)  

  xcos(x²)  

$\frac{1}{2}\cos\sqrt{x}$

$\frac{\left(2\sqrt{x}+1\right)}{4\sqrt{x+\sqrt{x}\ \ \sqrt{x}}}$

$\frac{1}{2}\sqrt{x}\cos\sqrt{x}$