More differentiation help needed!?

Question

Please differentiate f(x) = sinxsecx

Please show you working and answer clearly, 10 points for first correct and clear answer :) thanks in advance

Answer 1

f '(x) = cos(x)*sec(x) + sin(x)*sec(x)*tan(x)

        = 1 + [sin^2(x)]/[cos^2(x)]

Answer 2

f(x) = sin(x)*sec(x)

f '(x) = cos(x)*sec(x) + sin(x)*sec(x)*tan(x) = 1 + [sin(x)/cos(x)]^2 = 1/[cos^2(x)]

Answer 3

here...

as you know sec x  =1/ cos x, then

f(x) = sin x / cos x = tan x

d(tan x) / dx = sec^2 x, so...

f'(x) = sec^2 x

thx.

Answer 4

Use the product rule: derivative of the first function times the second function, plus the first function times the derivative of the second.

[cos(x)]sec(x) + sin(x)[sec(x)tan(x)]

This simplifies to

1 + [sin(x)/cos(x)]tan(x)

1 + tan(x)tan(x)

1 + tan^2(x)

sec^2(x)

This makes sense, because sin(x)sec(x) is just sin(x)/cos(x) = tan(x), and the derivative of tan(x) is sec^2(x).