$$\text { Find } \mathrm { dr } / \mathrm { d } \theta$$
-$\theta ^{4 / 3 }+ r ^ { 4 / 3 } = 1$
A) $- \left( \frac { \theta } { r } \right) ^ { 1 / 3 }$
B) $\left( \frac { r } { \theta } \right) ^ { 1 / 3 }$
C) $- \left( \frac { r } { \theta } \right) ^ { 1 / 3 }$
D) $\left( \frac { \theta } { r } \right) ^ { 1 / 3 }$

Question

Quizplus · Accepted Answer

To find $\frac{dr}{d\theta}$, we differentiate both sides of the equation $\theta^{4/3} + r^{4/3} = 1$ with respect to $\theta$, using implicit differentiation. Differentiating $\theta^{4/3}$ gives $\frac{4}{3}\theta^{1/3}$, and differentiating $r^{4/3}$ with respect to $\theta$ gives $\frac{4}{3}r^{1/3}\frac{dr}{d\theta}$. Setting the derivative of the right side (0) equal to the sum of these derivatives and solving for $\frac{dr}{d\theta}$ yields $-\left(\frac{\theta}{r}\right)^{1/3}$.

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

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