The rate of change of the function $f ( x ) = - \csc x - \sin x$is given by the expression $\csc x \cot x - \cos x$. Which of the following is its simplification?
A) $- \csc x \sec ^ { 2 } x$
B) $\tan ^ { 2 } x \cos x$
C) $\cot ^ { 2 } x \cos x$
D) $- \cot x \cos ^ { 2 } x$
E) $\sec ^ { 2 } x$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = -\csc x - \sin x$ simplifies to $\csc x \cot x - \cos x$, which can be further simplified to $\cot^2 x \cos x$ by recognizing that $\csc x \cot x = \cot^2 x$ when multiplied by $\cos x$, aligning with option C.

The Rate of Change of the Function f(x)=−csc⁡x−sin⁡xf ( x ) = - \csc x - \sin xf(x)=−cscx−sinx

The Rate of Change of the Function $f ( x ) = - \csc x - \sin x$