Differentiation - including trigonometric functions

$\sin x$

$-\sin x$

$-\operatorname{cosec}x\cot x$

$\sec2x$

$\operatorname{cosec}x\cot x$

$\sec x\tan x$

$\sec^2x$

$-\operatorname{cosec}x\cot x$

 $2x\sin2x+\cos2x$   

  $-2x\sin2x+\cos2x$  

 $\cos2x+4\sin2x$  

 $2x\cos2x$  

 $\frac{1}{6x+1}$  

 $\frac{6}{6x+1}$  

 $\frac{1}{6x}$  

6

 $e^{6x}$  

 $6e^{6x}$  

 $e^{6x-1}$  

 $6xe^{6x-1}$  

 $-\frac{1}{\left(2x+1\right)^2}$  

 $\frac{1}{\left(2x+1\right)^2}$  

 $\left(2x+1\right)^{-2}$  

 $2x+1$  

 $\frac{2}{2x+1}-\frac{2}{1-2x}$  

 $\frac{2}{2x+1}+\frac{2}{1-2x}$  

 $\frac{2}{2x-1}+\frac{2}{1-2x}$  

 $\frac{2}{2x+1}+\frac{2}{1+2x}$  

 $\frac{1}{2}\sqrt{1-3x^2}$  

 $\frac{1}{2\sqrt{1-3x^2}}$  

 $-\frac{3x}{\sqrt{1-3x^2}}$  

 $\frac{3}{2\sqrt{1-3x^2}}$  

 $8\tan^4\left(2x+1\right)\sec^2\left(2x+1\right)$  

 $2\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$  

 $4\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$  

 $8\tan^3\left(2x+1\right)\sec^2\left(2x+1\right)$  

dy/dx = -4 sin 4x

dy/dx=sin 4x

dy/dx = - 4 cos 4x

dy/dx = 4 sin 4x