Differentiate sin(x^3) with respect to y

For this we must use the chain rule. We start by defining x³ as a new variable, u = x³ Can then rewrite the expression as y = sin(u) Chain rule tells us that dy/dx = (dy/du)(du/dx) We can calculate these individidually. dy/du = cos(u)  du/dx = 3x² Finally we can then say, dy/dx = dy/du * du/dx = cos(u) * 3x² = 3x²cos(x³)