Question

How do you differentiate `f(x)=cscx * sec2x` using the product rule?

Answer 1

`(df)/(dx)=cscx(2sec2xtan2x-cotxsec2x)`

Explanation:

Product rule states if `f(x)=g(x)h(x)`

then `(df)/(dx)=(dg)/(dx)xxh(x)+(dh)/(dx)xxg(x)`

Hence as `f(x)=cscx*sec2x`

and `d/(dx)cscx=-cscxcotx` and `d/(dx)sec2x=sec2xtan2x xx2`

`:.(df)/(dx)=(-cscxcotx)xxsec2x+cscx xx sec2xtan2x xx 2`

= `cscx(2sec2xtan2x-cotxsec2x)`