Question

What is the derivative of `f(x) = 3x sec^2 x`?

Answer 1

`3sec^2x(1+2xtanx)`

Explanation:

we need the product rule here

`d/(dx)(uv)=v(du)/(dx)+u(dv)/(dx)`

`d/(dx)(3xsec^2x)=sec^2xd/(dx)(3x)+3xd/(dx)(sec^2x)`

`=(sec^2x) xx3+3x xx2secxtancsecx`

`=3sec^2x+6xsec^2xtanx`

`=3sec^2x(1+2xtanx)`