$$\text { Find } \mathrm { dr } / \mathrm { d } \theta$$
-$\cos ( r \theta ) + r ^ { 6 } = \theta ^ { 6 }$
A) $\frac { 6 r ^ { 5 } + \theta \sin r \theta } { 6 \theta ^ { 5 } - r \sin r \theta }$
B) $\frac { 6 r ^ { 5 } + r \sin r \theta } { 6 \theta ^ { 5 } }$
C) $\frac { 6 r ^ { 5 } - \theta \sin r \theta } { 6 \theta ^ { 5 } + r \sin r \theta }$
D) $\frac { 6 r ^ { 5 } - r \sin r \theta } { 6 \theta ^ { 5 } }$

Question

Quizplus · Accepted Answer

Using the chain rule, we have:

$$ \frac{dr}{d	heta}\cos{r	heta} -r\sin{r	heta}\frac{d(r	heta)}{d	heta} + 6r^5 = 6	heta^5 $$

Simplify and group the terms with $\frac{dr}{d	heta}$

$$ \frac{dr}{d	heta} = \frac{6	heta^5+r\sin{r	heta}}{\cos{r	heta}-6r^5} $$

Therefore the answer is $\boxed{	extbf{(C)}}$

Find dr/dθ\text { Find } \mathrm { dr } / \mathrm { d } \theta Find dr/dθ

$\text { Find } \mathrm { dr } / \mathrm { d } \theta$