Differentiate y=3 tan^4 x ?

1 Answer
maganbhai P.
Mar 6, 2018

#12[tan^3x+tan^5x]#

Explanation:

#(1)d/(dx)(x^n)=n*x^(n-1)#
#(2)d/(dx)(tanx)=sec^2x#
#y=3tan^4x=3(tanx)^4#
Let, #u=tanx#, then #(du)/(dx)=sec^2x# ,[Applying (2)]
Hence, #y=3u^4rArr(dy)/(du)=12u^3#, [Applying (1)]
#:.(dy)/(dx)=(dy)/(du)*(du)/(dx)=12u^3*sec^2x=color(red)(12tan^3xsec^2x)=12tan^3x(1+tan^2x)=12[tan^3x+tan^5x]#

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