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)
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