Derivatives of sinusoidal functions help?

Question

y=secx/ cos^2x I tried it but my answers is different than the back? Help

Answer 1

y = secx / cos²x

Recall : Trigonometry formulas secx = 1 / cosx then 1 / cos²x = sec²x

There fore y = secx (sec²x)

Simplify(power rule)

y = sec³x

Diferenciate with respective x to each side

Recall : Derivative formulas d/dx(xⁿ) = nx^n-1 and d/dx(secx) = secxtanx

dy /dx = 3sec²x secxtanx .1

dy / dx = 3sec³x sinx / cosx      (tanx = sinx / cosx)

dy / dx = 3sec³x sinx secx

dy / dx = 3sec⁴x sinx

dy / dx = 3sinx / cos⁴x

dy / dx  =3sinx / (cos²x)²       (cos²x = 1 - sin²x)

dy / dx = 3sinx / (1 - sin²x)²

dy / dx =3sinx / (1 - 2sin²x + sin⁴x) .