Question

Differentiation of y = sec⁴x

Answer 1

y = sec⁴x

we know , If any function y = {f(x)}^n given then,
differentiation of y, with respect to x
dy/dx = n.{ f(x)}^(n -1) .df(x)/dx
use this concept here,

y = ( secx)⁴

differentiate with respect to x
dy/dx = 4(secx)^(4-1).d(secx)/dx
=4.(secx)³.secx.tanx
=4(secx)⁴.tanx
=4sec⁴x.tanx

[ note :- differentiation of secx = secx.tanx]

Answer 2

Differentiation of y = sec⁴x

y = sec⁴x

dy/dx = 4 (secx)³ (secx tanx)

= 4sec⁴x.tanx