Question

Y=(x^2-1)/(x+2) производная

Answer 1

Y'=[2x*(x+2)-(x^2-1)*1 ] / (x+2)^2 = [2x^2+4x-x^2+1 ] / (x+2)^2 = [x^2+4x+1 ] /(x+2)^2

Answer 2

To find the derivative of the function Y with respect to x, we can use the quotient rule. The quotient rule states that if we have a function of the form u(x) / v(x), then its derivative is given by (v(x) * u'(x) - u(x) * v'(x)) / [v(x)]^2.

Let's apply the quotient rule to the function Y = (x^2 - 1) / (x + 2):

u(x) = x^2 - 1 (numerator) v(x) = x + 2 (denominator)

Now, let's find the derivatives of u(x) and v(x):

u'(x) = d/dx (x^2 - 1) = 2x v'(x) = d/dx (x + 2) = 1

Now, apply the quotient rule:

Y' = (v(x) * u'(x) - u(x) * v'(x)) / [v(x)]^2 Y' = [(x + 2) * 2x - (x^2 - 1) * 1] / (x + 2)^2 Y' = (2x^2 + 4x - x^2 + 1) / (x + 2)^2 Y' = (x^2 + 4x + 1) / (x + 2)^2

So, the derivative of the function Y with respect to x is Y' = (x^2 + 4x + 1) / (x + 2)^2.