Question

How do you differentiate `(2x+1)(x-tanx)`?

Answer 1

`d/(dx)(2x+1)(x-tanx)`

= `4x+1-2xsec^2x-sec^2x-2tanx`

Explanation:

If `f(x)=g(x)xxh(x)`, `(df)/(dx)=g(x)xx(dh)/(dx)+(dg)/(dx)xxh(x)`

Hence `d/(dx)(2x+1)(x-tanx)`

= `(2x+1)(1-sec^2x)+2(x-tanx)`

= `2x+1-2xsec^2x-sec^2x+2x-2tanx`

= `4x+1-2xsec^2x-sec^2x-2tanx`