2023 TWO(a)

Achievement
Question
Differentiate f(x)=x2cos⁡xf(x)=\dfrac{x^2}{\cos x}.

*You do not need to simplify your answer.*
Official Answer
f′(x)=(cos⁡x)(2x)−(x2)(−sin⁡x)cos⁡2xf'(x)=\dfrac{(\cos x)(2x)-(x^2)(-\sin x)}{\cos^2 x}
=2xcos⁡x+x2sin⁡xcos⁡2x=\dfrac{2x\cos x+x^2\sin x}{\cos^2 x}
=x(2cos⁡x+xsin⁡x)cos⁡2x=\dfrac{x(2\cos x+x\sin x)}{\cos^2 x}
Grading Criteria

Achievement (u)

  • Correct derivative.

Merit (r)

-

Excellence T1

-

Excellence T2

-
Video Explanation
2023 NCEA L3 Calculus Exam Walkthrough by infinityplusone(starts at 29:15)
Subscribe
Exam Paper (2023)Assessment Schedule (2023)
Related Questions
2024 THREE(c)Merit

Find the $x$-value(s) of any stationary point(s) on the graph of the function $f(x)=\dfrac{x^2-5x+4...

2024 THREE(b)Achievement

The graph below shows the function $y = f(x)$. [DIAGRAM] (i) For the function above, find the valu...

2024 TWO(e)Excellence

The graph of the function $y = \dfrac{xe^{3x}}{2x + k}$, where $k$ is a non-zero constant, has a sin...

2024 TWO(a)Achievement

A function is defined parametrically by the pair of equations: $x = 3t^2 + 1$ and $y = \cos t.$ Fi...

2024 ONE(b)Achievement

A curve is defined by the equation $y = (x^2 + 3x + 2)\,\sin x$. Find the gradient of the tangent t...