Find the derivative of the function y = – 9x ^ 4 + 3x ^ 2 – 10 at the point x0 = -2.

First, we calculate the derivative of the given function, and then find its value at the point X0 = -2.

Y = -9X ^ 4 + 3X ^ 2 – 10.

According to the rule for finding the derivative, we will lower the degree of each term of the polynomial, taking the degree forward.

Y ‘= -9 * (X ^ 4)’ + 3 * (X ^ 2) ‘- 10’.

Y ‘= -9 * 4 * X ^ 3 + 3 * 2 * X1 – 0.

Y ‘= -36X ^ 3 + 6X.

Now we calculate Y ‘(X0).

Y ‘(- 2) = -36 * (-2) ^ 3 + 6 * (-2).

Y ‘(- 2) = – 36 * (-8) – 12.

Y ‘(- 2) = 288 – 12.

Y ‘(- 2) = 276.