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Solution assignment 16 Chain rule

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Assignment 16

Differentiate:

y=\tan(3x)

Solution

Earlier, when we discussed the topic Product and Quotient rule, we calculated:

[\tan(x)]'=\displaystyle\frac{1}{\cos^2(x)}

or:

[\tan(x)]'=1-\tan^2(x)

Thus for the function above we get:

y'=\displaystyle\frac{1}{\cos^2(3x)}\cdot3=\displaystyle\frac{3}{\cos^2(x)}

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