Support Prove by differentiation that if F(x) and G(x) are primitives of f(x) and g(x), and k is a constant, then F(x) + G(x) is a primitive of f(x) + g(x), and kF(x) is a primitive of kf(x)

Resources for the prerequisite content of this dot point: earlier-stage (or earlier sub-level) dot points in the same strand that students usually need first. Use these to fill gaps before or alongside the core lesson.

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Prerequisite dot points

Apply the chain rule: if y is a differentiable function of u, and u is a differentiable function of x, then dy/dx = dy/du × du/dx or if h(x) = f(g(x)) for differentiable functions f(x) and g(x) then h'(x) = f'(g(x))g'(x)

Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping

No checked resources on this prerequisite dot point yet.

Apply the product rule: if y = uv, where u and v are both differentiable functions of x, then dy/dx = udv/dx + vdu/dx or if h(x) = f(x)g(x) for differentiable functions f(x) and g(x) then h'(x) = f(x)g'(x) + f'(x)g(x)

Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping

No checked resources on this prerequisite dot point yet.

Apply the quotient rule: if y = u/v, where u and v are both differentiable functions of x, then dy/dx = (vdu/dx - udv/dx)/v² or if h(x) = (f(x))/(g(x)) then h'(x) = (g(x)f^'(x) - f(x)g^'(x))/([(g(x)])²)

Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping

No checked resources on this prerequisite dot point yet.