Level 3 Differentiation Walkthrough

2016 NCEA Level 3 Differentiation Question 2(b)

2016 Paper

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Question

Find the gradient of the tangent to the function

\[y=\sqrt{2x-1}\]

at the point \((5,3)\).

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

First walkthrough idea

Focus to try first

Rewrite the square root as a power, differentiate with the chain rule, then substitute \(x=5\).

Step 1

Rewrite the radical

Power notation makes the outside function explicit.

Show the first step’s working
\[y=(2x-1)^{1/2}.\]

Walkthrough overview

What this question practises

This 2016 walkthrough is part of AS91578 — Apply differentiation methods in solving problems.

Method: Chain rule differentiation of a square-root function.

This is Question 2(b) from the 2016 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.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise chain rule differentiation of a square-root function. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Do not stop after differentiating the outside function; include the derivative of the inside function as a factor.

Continue practising

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