If y = 1/(x^2) + 4x, find dy/dx

First, notice that 1/(x^2) = x^(-2)

dy/dx = d/dx (x^(-2) + 4x)

The derivative of the sum is the sum of the derivatives

= d/dx (x^(-2)) + d/dx (4x)

The derivative of x^n is nx^(n-1), for every real number n, and a constant gets in front of the deivative

= -2 x^(-3) + 4 d/dx (x)

= -2/(x^3) + 4

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