Differentiation of y=√(sin³x) ?

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Answer 1 · 2018-05-03T08:33:36

#(dy)/(dx)=3/2sqrt((sinx))*(cosx)#

Here,

#y=√(sin³x)#

#i.e. y=sqrt((sinx)^3)=((sinx)^3)^(1/2)#

Diff.w.r.t. #x#, #"using "color(blue)"Chain Rule :"#

#=>y=(sinx)^(3/2)...to[ As, (a^m)^n=a^(mn) ]#

#:.(dy)/(dx)=3/2(sinx)^(3/2-1)d/(dx)(sinx)#

#=>(dy)/(dx)=3/2(sinx)^(1/2)(cosx)#

#=>(dy)/(dx)=3/2sqrt((sinx))*(cosx)#