What is the derivative of #tan^5(x)#?

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What is the derivative of #tan^5(x)#?

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Answer 1 · 2018-03-21T18:03:38

#y=tan^5x=(tanx)^5=>dy/dx=5(tanx)^4d/(dx)(tanx)#
#=>dy/dx=5tan^4x*sec^2x#

Explanation:

Let,
#y=tan^5x=(tanx)^5#
We take,
#y=u^5,# where, #u=tanx#
#=>(dy)/(du)=5u^4 and (du)/(dx)=sec^2x#
Applying chain rule
#dy/dx=dy/(du)*(du)/dx#
#=>dy/dx=5u^4*sec^2x#
#=>dy/dx=5(tanx)^4*sec^2x#
#=>dy/dx=5tan^4xsec^2x#

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What is the derivative of #tan^5(x)#?

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