Find the derivative of y with respect to the independent variable.
-$$y = ( \cos \theta ) ^{\sqrt { 11} }$$
A) $\sqrt { 11 } ( \cos \theta )^{ \sqrt { 11 } - 1}$
B) $- \sqrt { 11 } \cos \theta \sin \theta$
C) $- ( \cos \theta )^{ \sqrt { 11 } - 1 }\sin \theta$
D) $- \sqrt { 11 } ( \cos \theta )^{ \sqrt { 11 } - 1} \sin \theta$

Question

Quizplus · Accepted Answer

Using the chain rule, we have:

$$\frac{dy}{d	heta} = \frac{d}{d	heta}[(\cos 	heta)^{\sqrt{11}}] = (\sqrt{11})(\cos 	heta)^{\sqrt{11}-1}(-\sin 	heta) = -\sqrt{11}(\cos 	heta)^{\sqrt{11}-1}\sin 	heta$$

Therefore, the correct answer is choice D.

Find the Derivative of Y with Respect to the Independent y=(cos⁡θ)11y = ( \cos \theta ) ^{\sqrt { 11} }y=(cosθ)11​

Find the Derivative of Y with Respect to the Independent $y = ( \cos \theta ) ^{\sqrt { 11} }$