Find dy.
-$$y = 3 \cot \left( \frac { 1 } { 3 } x ^ { 3 } \right)$$
A) $- 3 x ^ { 3 } \csc ^ { 2 } \left( \frac { 1 } { 3 } x ^ { 3 } \right) d x$
B) $3 x ^ { 2 } \csc ^ { 2 } \left( \frac { 1 } { 3 } x ^ { 3 } \right) d x$
C) $- 3 x ^ { 2 } \csc ^ { 2 } \left( \frac { 1 } { 3 } x ^ { 3 } \right) d x$
D) $- 3 x ^ { 2 } \csc \left( \frac { 1 } { 3 } x ^ { 3 } \right) d x$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$ for $y = 3 \cot \left( \frac { 1 } { 3 } x ^ { 3 } \right)$, we use the chain rule. The derivative of $\cot(u)$ is $-\csc^2(u)$, and the derivative of $\frac{1}{3}x^3$ with respect to $x$ is $x^2$. Thus, $\frac{dy}{dx} = 3 \cdot (-\csc^2(\frac{1}{3}x^3)) \cdot (x^2) = -3x^2\csc^2(\frac{1}{3}x^3)$.

Find Dy - y=3cot⁡(13x3)y = 3 \cot \left( \frac { 1 } { 3 } x ^ { 3 } \right)y=3cot(31​x3)

Find Dy
- $y = 3 \cot \left( \frac { 1 } { 3 } x ^ { 3 } \right)$