Question

How do you differentiate `y=sinxsecx`?

Answer 1

y'= `sec^2 x`

Explanation:

Write y=`sinx /cos x`= tan x and use standard formula for the derivative of tan x

Answer 2

If you didn't want to take the derivative of `tanx`, or you know the derivative of `secx` better:

`d/(dx)[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)`

`(dy)/(dx) = (sinx)(secxtanx) + secxcosx`

`= tan^2x + 1`

`= color(blue)(sec^2x)`