How do you take the derivative of $tan3x$ ?

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Answer 1 · 2015-06-18T12:50:06

Use the chain rule and the fact that the derivative of the tangent function is the square of the secant function.

I recommend memorizing this:
$d/dx(tanx) =sec^2 x$

Applying the chain rule, we get

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

In this problem, we have $u = 3x$ , so $(du)/dx = 3$

Now we put these pieces together to see that the derivative of $tan 3x$ is

$d/dx(tan 3x) = (sec 3x ) * 3$ , which is more clear if we write it as:

$d/dx(tan 3x) = 3sec 3x$

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