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Numerade Educator

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Problem 30 Easy Difficulty

Find the derivative of the function.
$ J(\theta) = \tan^2 (n \theta) $

Answer

2$n \tan (n \theta) \sec ^{2}(n \theta)$

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Video Transcript

all right. So here we have J of data and it's a composite function. We have a function inside of function. Actually, we have three layers function inside a function inside function. So we're going to use the chain rule to find the derivative. I remember when you see Tangent Square data, what it means actually is you're taking the tangent in this case of in data and that whole thing is being squared the square it is actually on the very outside. That's our outermost function. So now, to find the derivative, what we want to do is use the chain rule, first of all, the derivative of the squaring function, bring down the two and then raised tangent of Anthea to the first. And then we multiply by the derivative of the tangent and derivative of tangent is he can't squared. So we multiply by c can't squared of Anthea and then we multiply by the derivative of the very inside part the derivative of in data is in. So if we write that in a simplified way, by just multiplying the two and the end together we have to end times the tangent of and data times a C can't squared of in data