What is the derivative of y=x sec(kx)?

3 Answers
Mar 23, 2018

As below.

Explanation:

Differentiating y w.r.t. x,

#dy/dx=x.{d/dxsec(kx)×d/dxkx}+sec(kx)×(d/dx)x#

=x*seckxtankx×k + seckx

=seckx(kxtankx+1)

=>sec(kx) (1 + kx*tankx)

Explanation:

Using product rule,

d(xsec(kx))/dx = d(x)/dxsec(kx) + xd(sec(kx))/dx

d(xsec(kx))/dx = sec(kx) + x*k*tankx*seckx

=> sec (kx) ( 1 + kx tan (kx))

Mar 23, 2018

(1+kxtan(kx))/cos(kx)

Explanation:

y=x/cos(kx)

y=u/v
y'=(v*u'-v'*u)/v^2

u=x
u'=1
v=cos(kx)
v'=-ksin(kx)

y'=(cos(ks)+kxsin(kx))/(cos(kx)^2) =(1+kxtan(kx))/cos(kx)