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How do you take the derivative of #tan^10 5x#?

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Jun 17, 2015

Consider the regular derivative of #tanu#.

#d/(dx)[tanu] = sec^2u*((du)/(dx))#

Since #u(x) = 5x# and we have a power function:

#d/(dx)[(tanu)^n] = n(tanu)^(n-1)*sec^2u*((du)/(dx))#

#d/(dx)[(tan(5x))^(10)] = 10(tan(5x))^9*sec^2(5x)*5#

#= 50tan^9(5x)sec^2(5x)#

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