Let $$ f(x)=2 \csc (6 x) $$ $$ f^{\prime}(x)=\square $$

Question

UpStudy AI · Accepted Answer

To find the derivative of f(x) = 2 csc(6x), follow these steps:

1. Recognize that the derivative of csc(u) with respect to u is –csc(u) cot(u).
2. Use the chain rule: if u = 6x, then du/dx = 6.

Thus, differentiating f(x) = 2 csc(6x):

f′(x) = 2 · [d/dx (csc(6x))]
       = 2 · [–csc(6x) cot(6x) · 6]
       = –12 csc(6x) cot(6x).

So, the final answer is:

f′(x) = –12 csc(6x) cot(6x).
The derivative of $$ f(x) = 2 \csc(6x) $$ is $$ f'(x) = -12 \csc(6x) \cot(6x) $$.

Let \( f(x)=2 \csc (6 x) \) \( f^{\prime}(x)=\square \)