Math Calculus please?

Question

Given y = [(x^3)(x^2 + 1)]^3 calculate the instantaneous rate of change of this function when x = 2.

The instantaneous rate of change is _________

Answer 1

The equation is y = [x³(x² + 1)]³.

Differentiate with respect to x.

y' = 3[x³(x² + 1)]² * (d/dx)[x³(x² + 1)].

y' = 3[x³(x² + 1)]² * [x³ * 2x + (x²+1) * 3x²].

y' = 3[x⁵ + x³]² * [5x⁴ + 3x²].

Substitute x = 2 in the above equation.

y' = 3[2⁵ + 2³]² * [5*2⁴ + 3*2²] = (4800)(92) = 441600.

The instantaneous rate of change of this function at x = 2 is 441600.