SOLUTION: Calculus Question Find {{{ D^132[sin(7x)] }}}. (a) {{{ -7^132sin(7x) }}} (b) {{{ 7^132sin(7x) }}} (c) {{{ -7^132cos(7x) }}} (d) {{{ -7^132cos(7x) }}} (e) None of these ar

Algebra ->  Equations -> SOLUTION: Calculus Question Find {{{ D^132[sin(7x)] }}}. (a) {{{ -7^132sin(7x) }}} (b) {{{ 7^132sin(7x) }}} (c) {{{ -7^132cos(7x) }}} (d) {{{ -7^132cos(7x) }}} (e) None of these ar      Log On


   

Question 1142314: Calculus Question
Find +D%5E132%5Bsin%287x%29%5D+.
(a) +-7%5E132sin%287x%29+
(b) +7%5E132sin%287x%29+
(c) +-7%5E132cos%287x%29+
(d) +-7%5E132cos%287x%29+
(e) None of these are correct.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


NOTE: You have apparently shown the answer choices incorrectly, since choices c and d are identical....

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.

So the question is whether the 132nd derivative is sine or cosine, and whether it is positive or negative.

The pattern of sine/cosine and positive/negative repeats in a cycle of 4:

D(1) = cos
D(2) = -sin
D(3) = -cos
D(4) = sin
D(5) = cos
D(6) = -sin
...

So which function and which sign does D(132) have?