Question

Y=arccos(2x^2-3)Найти производную​

Answer 1

y'=-1/sqrt(1-(2x^2-3)^2) * (2x^2-3)' = -4x/sqrt(1-(2x^2-3)^2)

Answer 2

To find the derivative of the given function Y = arccos(2x^2 - 3), we'll use the chain rule. The chain rule states that if we have a composition of functions, say g(f(x)), then the derivative with respect to x is given by g'(f(x)) * f'(x). In this case, our outer function is arccos(u), and our inner function is (2x^2 - 3).

Let's proceed with finding the derivative step by step:

Step 1: Find the derivative of the inner function (2x^2 - 3) with respect to x. d/dx (2x^2 - 3) = 4x.

Step 2: Find the derivative of the outer function arccos(u) with respect to u. d/du (arccos(u)) = -1 / sqrt(1 - u^2).

Step 3: Apply the chain rule by multiplying the derivatives found in Step 1 and Step 2: dy/dx = (d/du (arccos(u))) * (d/dx (2x^2 - 3)) dy/dx = (-1 / sqrt(1 - (2x^2 - 3)^2)) * 4x.

So, the derivative of Y with respect to x is dy/dx = -4x / sqrt(1 - (2x^2 - 3)^2).