What is the Derivative of a×sec^3x?

1 Answer
Shiva Prakash M V
Mar 6, 2018

#d/dx(asec^3x)=3asec^3xtanx#

Explanation:

Given:
#y=asec^3x#
To find:
#dy/dx#
#dy/dx=d/dx(y)#
#d/dx(y)=d/dx(asec^3x)#
By constant rule
#d/dx(asec^3x)=ad/dx(sec^3x)#
By index rule
#ad/dx(sec^3x)=ad/dx(secx)^3#
Let
#t=secx#
#dt/dx=secxtanx#
#=ad/dx(secx)^3=ad/dx(t^3)#
#d/dx(t^3)=3t^2dt/dx#
#ad/dx(t^3)=a(3t^2)dt/dx#
Substituting for t and dt/dx
#ad/dx((secx)^3)=a(3(secx)^2)(secxtanx)#
Simplifying
#d/dx(asec^3x)=3asec^3xtanx#

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