Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ .
A) $\sin x + \sec x$
B) $\sin x + 1$
C) $\sin x - \tan x \sec x$
D) $\sin x \sin x$
E) $\csc x \cot x - \sin x$

Question

Find the rate of change of the function $f ( x ) = - \csc x - \cos x$ . ​
A)​ $\sin x + \sec x$
B)​ $\sin x + 1$
C)​ $\sin x - \tan x \sec x$
D)​ $\sin x \sin x$
E)​ $\csc x \cot x - \sin x$

Quizplus · Accepted Answer

The rate of change of a function is found by taking its derivative. For $f(x) = -\csc x - \cos x$, the derivative $f'(x)$ is found by applying the derivatives of $-\csc x$ and $-\cos x$ separately. The derivative of $-\csc x$ is $\csc x \cot x$, and the derivative of $-\cos x$ is $\sin x$. Therefore, $f'(x) = \csc x \cot x - \sin x$.

Find the Rate of Change of the Function f(x)=−csc⁡x−cos⁡xf ( x ) = - \csc x - \cos xf(x)=−cscx−cosx

Find the Rate of Change of the Function $f ( x ) = - \csc x - \cos x$