Question
Y=1-
(×-2)^2
Using differentiation to solve
(×-2)^2
Using differentiation to solve
Answers
GPT 3.5
To find the derivative of Y=1-(x-2)^2, we first need to expand the square term using the formula (a-b)^2 = a^2 - 2ab + b^2.
Y = 1 - (x^2 - 4x + 4)
Y = 1 - x^2 + 4x - 4
Y = -x^2 + 4x - 3
Now, we can differentiate Y with respect to x:
d/dx(-x^2 + 4x - 3) = -2x + 4
Therefore, the derivative of Y=1-(x-2)^2 is -2x + 4.
Y = 1 - (x^2 - 4x + 4)
Y = 1 - x^2 + 4x - 4
Y = -x^2 + 4x - 3
Now, we can differentiate Y with respect to x:
d/dx(-x^2 + 4x - 3) = -2x + 4
Therefore, the derivative of Y=1-(x-2)^2 is -2x + 4.