# Differentiation Of Trigonometric Functions Homework

Note that we didn’t really need to do a change of variables here.All we really need to notice is that the argument of the sine is the same as the denominator and then we can use the fact.$\mathop \limits_ \frac = \mathop \limits_ \frac = 6\mathop \limits_ \frac$ Note that we factored the 6 in the numerator out of the limit.

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A change of variables, in this case, is really only needed to make it clear that the fact does work.

In this case we appear to have a small problem in that the function we’re taking the limit of here is upside down compared to that in the fact.

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With this section we’re going to start looking at the derivatives of functions other than polynomials or roots of polynomials.

This is not the problem it appears to be once we notice that, $\frac = \frac$ and then all we need to do is recall a nice property of limits that allows us to do , $\begin\mathop \limits_ \frac & = \mathop \limits_ \frac\\ & = \frac\\ & = \frac\end$ With a little rewriting we can see that we do in fact end up needing to do a limit like the one we did in the previous part.

## Differentiation Of Trigonometric Functions Homework

So, let’s do the limit here and this time we won’t bother with a change of variable to help us out.

We’ll start this process off by taking a look at the derivatives of the six trig functions. The remaining four are left to you and will follow similar proofs for the two given here.

Before we actually get into the derivatives of the trig functions we need to give a couple of limits that will show up in the derivation of two of the derivatives.

So we need to get both of the argument of the sine and the denominator to be the same.

We can do this by multiplying the numerator and the denominator by 6 as follows.

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