Question

Find the derivative y=2xcotx

Answer 1

product rule

Answer 2

2(cotx)+(-csc^2x)(2x)

Answer 3

Questions for you tech-dodo:

1) What is the derivative of 2x ?
2) What is the derivative of cot(x) ?
3) What is the product rule for taking derivatives of the product of two functions?

Answer 4

\begin{eqnarray*}y' &=& (2x\cot x)'\\&=&(2x)'\cot x+2x(\cot x)'\\&=&2\cot x+2x\left(\frac{\cos x}{\sin x}\right)'\\&=& 2\cot x+2x\frac{(\cos x)'\sin x-(\sin x)'\cos x}{\sin^2x}\\&=&2\cot x+2x\frac{-\sin x\sin x-\cos x\cos x}{\sin^2x}\\&=&2\cot x-2x\frac{\sin^2x+\cos^2x}{\sin^2x}\\&=&2\left(\cot x-\frac{x}{\sin^2x}\right)\\&=&2\left(\cot x-x \csc^2x\right).\end{eqnarray*}

Answer 5

You are lighting fast with LaTeX, Krebante! :D