Suppose f(x)= 1/u^3 , where u=x^3 + 2. Determine a simplified expression for the slope of all tangents to y = f(x).
f = u^-3, so df/du = -3u^-4
df/dx = df/du * du/dx = -3/u^4 * u' = -3/u^4 * 3x^2 = -9x^2/(x^3+2)^4
df/dx = df/du * du/dx = -3/u^4 * u' = -3/u^4 * 3x^2 = -9x^2/(x^3+2)^4