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Y prime equals 9.
Remember the derivative of secon X is secant tangent, so Y prime
is 9, secon X tangent XY double prime.
We have to take the nine times the derivative of the secon X
which is secant tangent times the tangent.
Plus, by the product rule 9 secon X times the derivative of
tangent X, which is secant squared X.
So we get 9 secant X tangent squared X + 9 secant cubed X.
By our Pythagorean identity, we know that secant squared X is
really no, sorry.
By our Pythagorean identity, we know that tangent squared X is
really just secant squared X -, 1.
So when we distribute the 9 secant X, we get 9 secant cubed
X -, 9 secant X + 9 secant cubed X.
We get 18 secant cubed X -, 9 secant X.