What is the (tan^3(x))^' ?

The (tan^3(x))^' is 3tan^2(x)sec^2(x)

What is the first (tan^3(x))^' ?

The first (tan^3(x))^' is 3tan^2(x)sec^2(x)

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(tan^{3} (x))^{^{'}}

3 tan^{2} (x) sec^{2} (x)

Solution steps

(tan^{3} (x))^{'}

Apply the chain rule:

3 (tan (x))^{2} (tan (x))^{'}

= 3 (tan (x))^{2} (tan (x))^{'}

(tan (x))^{'} = sec^{2} (x)

= 3 (tan (x))^{2} sec^{2} (x)

Simplify

= 3 tan^{2} (x) sec^{2} (x)

4 t e^{- 2 t}

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\frac{10 s}{s ^{2} + 16}