If Y = SecXTanX, find y" 4y' 4y.

Question

I can easily do the second part of the question if I could if only I could find d first and second derivative of SecXTanX, pls do help.

Answer 1

well, finding y' and y'' is really the main part of the meal, the rest is just cleaning the dishes.

you should know the derivatives of the 6 basic trig functions by heart.

y' = secx(sec^2 x) + tanx(secxtanx) , by the product rule
= sec^3 x + tan^2 x secx

y'' = 3(sec^2 x)(secxtanx) + tan^2 x(secxtanx) + (secx)(2)(tanx)(sec^2 x)
= 3 sec^3 x tanx + secx tan^3 x + 2(sec^3 x)tanx
= 5sec^3 x tanx + secx tan^3 x

carry on