Question

一道数学对数的证明题.Y＝In（sec x＋tan x） 证明dy/dx=secx

Answer 1

Let secx + tanx = u

Y = ln (secx+tanx) = ln u

dy/dx = d(ln u)/dx = (1/u)*du/dx

=(1/(secx + tanx)) * d(secx+tanx)/dx

=(1/(secx + tanx)) * [(dsecx + dtanx)/dx]

=(1/(secx + tanx)) * (secx*tanx + sec^2(x))

= secx(secx + tanx)/(secx + tanx)

= secx (yeah!)