Find dy.
-$$y = \csc \left( 6 x ^ { 2 } - 1 \right)$$
A) $- 12 x \csc ( 12 x ) \cot ( 12 x ) d x$
B) $- 6 x ^ { 2 } \csc \left( 6 x ^ { 2 } - 1 \right) \cot \left( 6 x ^ { 2 } - 1 \right) d x$
C) $- 12 x \csc \left( 6 x ^ { 2 } - 1 \right) \cot \left( 6 x ^ { 2 } - 1 \right) d x$
D) $12 x \csc \left( 6 x ^ { 2 } - 1 \right) \cot \left( 6 x ^ { 2 } - 1 \right) d x$

Question

Quizplus · Accepted Answer

We can use the chain rule to find $dy$:
\begin{align*}
\frac{d}{dx} \left( \csc (6x^2-1) ight) &= -\csc (6x^2-1) \cot (6x^2-1) \cdot \frac{d}{dx} (6x^2-1) \
&= -\csc (6x^2-1) \cot (6x^2-1) \cdot 12x \
&= -12x \csc (6x^2-1) \cot (6x^2-1)
\end{align*}
Therefore, the answer is (C).

Find Dy - y=csc⁡(6x2−1)y = \csc \left( 6 x ^ { 2 } - 1 \right)y=csc(6x2−1)

Find Dy
- $y = \csc \left( 6 x ^ { 2 } - 1 \right)$