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

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Answer 1 · 2015-06-17T00:17:10

Consider the regular derivative of $tanu$ .

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

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

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

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

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

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