Find all possible functions with the given derivative.
-$y ^ { \prime } = \csc ^ { 2 } 3 \theta$
A) $- 3 \cot 3 \theta + C$
B) $\frac { 1 } { 6 } \csc 3 \theta + C$
C) $- \frac { 1 } { 3 } \cot 3 \theta + C$
D) $- \frac { 1 } { 9 } \csc ^ { 3 } 3 \theta + C$

Question

Quizplus · Accepted Answer

We know that the derivative of $\cot \theta$ is $-\csc^2 \theta$, so by integrating both sides we get:
$$y = -\frac{1}{3}\cot 3\theta + C$$
Therefore, the only possible choice is C.

Find All Possible Functions with the Given Derivative y′=csc⁡23θy ^ { \prime } = \csc ^ { 2 } 3 \thetay′=csc23θ

Find All Possible Functions with the Given Derivative $y ^ { \prime } = \csc ^ { 2 } 3 \theta$