Level 3 Differentiation Walkthrough

2018 NCEA Level 3 Differentiation Question 3(d)

2018 Paper

← Back to paper

Question

Find the equation of the tangent to the curve

\[y=x^2\ln x\]

at the point where \(x=e\).

You must use calculus and show any derivatives that you need to find when solving this problem.

First walkthrough idea

Focus to try first

Find the point on the curve and the derivative at \(x=e\), then use point-gradient form.

Step 1

Find the point

Substitute \(x=e\) into the curve and use \(\ln e=1\).

Show the first step’s working
\[y=e^2\ln e=e^2\quad\Longrightarrow\quad (e,e^2)\]

Walkthrough overview

What this question practises

This 2018 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Product rule and the equation of a tangent.

This is Question 3(d) from the 2018 NCEA Level 3 Differentiation paper for AS91578 — Apply differentiation methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91578.

Page updated .

Learning summary

Review the method, not only the answer

This walkthrough helps you practise product rule and the equation of a tangent. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Differentiate both factors in turn and keep both product-rule terms.

Continue practising

← Question 3(c) Question 3(e) →