<PRE><B>Question 1142314</B>
&lt;br&gt;
NOTE: You have apparently shown the answer choices incorrectly, since choices c and d are identical....&lt;br&gt;
From the chain rule, it is clear that each derivative is going to produce a factor of 7.  So 7^132 is part of the answer.&lt;br&gt;
So the question is whether the 132nd derivative is sine or cosine, and whether it is positive or negative.&lt;br&gt;
The pattern of sine/cosine and positive/negative repeats in a cycle of 4:&lt;br&gt;
D(1) = cos
D(2) = -sin
D(3) = -cos
D(4) = sin
D(5) = cos
D(6) = -sin
...&lt;br&gt;
So which function and which sign does D(132) have?
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