Find the derivative.
-$$r = 20 - \theta ^ { 4 } \cos \theta$$
A) $\frac { \mathrm { dr } } { \mathrm { d } \theta } = 4 \theta ^ { 3 } \sin \theta - \theta ^ { 4 } \cos \theta$
B) $\frac { \mathrm { dr } } { \mathrm { d } \theta } = 4 \theta ^ { 3 } \sin \theta$
C) $\frac { \mathrm { dr } } { \mathrm { d } \theta } = 4 \theta ^ { 3 } \cos \theta - \theta ^ { 4 } \sin \theta$
D) $\frac { \mathrm { dr } } { \mathrm { d } \theta } = - 4 \theta ^ { 3 } \cos \theta + \theta ^ { 4 } \sin \theta$

Question

Quizplus · Accepted Answer

To find the derivative of $r = 20 - \theta^4 \cos \theta$ with respect to $\theta$, we apply the product rule and the chain rule. The derivative of a constant is 0, and for $\theta^4 \cos \theta$, we use the product rule: $\frac{d}{d\theta}(\theta^4 \cos \theta) = 4\theta^3 \cos \theta - \theta^4 \sin \theta$. Thus, the derivative of $r$ is $\frac{dr}{d\theta} = - 4\theta^3 \cos \theta + \theta^4 \sin \theta$.

Find the Derivative r=20−θ4cos⁡θr = 20 - \theta ^ { 4 } \cos \thetar=20−θ4cosθ

Find the Derivative $r = 20 - \theta ^ { 4 } \cos \theta$