Question

Let y=x/(1+x^2)+1/sin(x). Find dy/dx.

Answer 1

\[y=\frac{ x }{ 1+x² }+\frac{ 1 }{ \sin(x) }\]

Answer 2

so using the sum rule and then the quotient rule on the two different parts...

Answer 3

\[D \left( \frac{ x }{ 1+x² } \right)=\frac{ (1+x²)*1-(x*2x) }{ (1+x²)² }=\frac{ 1-x² }{ (x²+1)² }\]

Answer 4

I really suck at trig identities

Answer 5

\[\huge \frac1{\sin x}=\csc x\]
You know the derivative of cosecant?

Answer 6

You can also thinnk of 1/sinx as a quotient rule; however, it's much easier to recall the derivative of cscx instead.