The correct response is:
dy/dx = -2csc(2x√)cot(2x√)√
dy/dx = -2csc(2x√)cot(2x√)√
Let u = 2x-√
Now, we can rewrite the function as y = csc(u)
The derivative of csc(u) with respect to u is -csc(u)cot(u).
Now, let's find the derivative of u with respect to x.
du/dx = d(2x-√)/dx
= 2-√ * d(2x)/dx
= 2-√ * 2
= 4-√
Finally, we can apply the chain rule:
dy/dx = (dy/du) * (du/dx)
= -csc(u) * cot(u) * 4-√
= -4-√ * csc(2x-√) * cot(2x-√)
Therefore, the answer is: dy/dx = -4-√ * csc(2x-√) * cot(2x-√)
First, let's find the derivative of the outer function. The derivative of csc(u) is -csc(u)cot(u), where u represents the input of the csc function.
Next, let's differentiate the inner function. The derivative of 2x-√ is simply 2.
Now, we can apply the chain rule. The derivative of y = csc(2x-√) is given by:
dy/dx = d(csc(2x-√))/d(2x-√) * d(2x-√)/dx
Using the derivatives we found earlier, we have:
dy/dx = -csc(2x-√)cot(2x-√) * 2
Therefore, the correct answer is: dy/dx = -2csc(2x-√)cot(2x-√).