Support · Mathematics Extension 1 11–12 – Year 12 · Further calculus skills
Support Verify using the chain rule that the derivative of the inverse function is the reciprocal of the derivative of the function, evaluated at the value of the inverse function, that is (f^(- 1))'(x) = 1/(f^'(f^(- 1)(x)))
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Prerequisite dot points
Use chain rule on the identity e^(lnx) = x to prove the formula d/dx(lnx) = 1/x for the derivative of the natural logarithm function where x > 0
Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping
No checked resources on this prerequisite dot point yet.
Apply the fact that the derivative of a sum is the sum of the derivatives: d/dx(f(x) + g(x)) = f'(x) + g'(x), and the derivative of a multiple of a function is the multiple of its derivative: d/dx(k⋅f(x)) = k⋅f'(x)
Mathematics Advanced 11–12 – Year 11 · Introduction to differentiation Draft mapping
No checked resources on this prerequisite dot point yet.
Use the chain rule to differentiate functions of the form lnf(x)
Mathematics Advanced 11–12 – Year 12 · Differential calculus Draft mapping
No checked resources on this prerequisite dot point yet.