Question #d8431

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Answer 1 · 2017-02-17T13:03:06

#d/dx sec^3(sqrt(cosx)) = -(3sinxsec^3(sqrt(cosx)) tan (sqrt(cosx)) )/(2sqrt(cosx)) #

#d/dx sec^3(sqrt(cosx)) = d/(du) u^3 * d/(dy) sec y * d/(dt) sqrt(t) d/dx cosx#

where:

#u= sec(sqrt(cosx))#

#y= sqrt(cosx)#

#t = cosx#

so:

#d/dx sec^3(sqrt(cosx)) = 3u^2 * secy tany * 1/(2sqrt(t)) * (-sinx)#

#d/dx sec^3(sqrt(cosx)) = 3sec^2(sqrt(cosx)) * sec(sqrt(cosx)) tan (sqrt(cosx)) * 1/(2sqrt(cosx)) * (-sinx)#

#d/dx sec^3(sqrt(cosx)) = -(3sinxsec^3(sqrt(cosx)) tan (sqrt(cosx)) )/(2sqrt(cosx)) #