NCEA Calculus 2019 ONE(c - Solution & Explanation

Question

Find the gradient of the tangent to the curve

y = \dfrac{e^{2x}}{1+x^2}

at the point where

x = 2

.

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

Official Answer

Quotient rule

\dfrac{dy}{dx}=\dfrac{(1+x^2)2e^{2x}-e^{2x}(2x)}{(1+x^2)^2}

OR

Product rule

\dfrac{dy}{dx}=e^{2x}(-2x)(1+x^2)^{-2}+(1+x^2)^{-1}(2e^{2x})

When

x=2

,

\dfrac{dy}{dx}=\dfrac{6e^4}{25}

or

13.1

Grading Criteria

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Video Explanation

NCEA Level 3 Calculus Differentiation 2019 NZQA Exam - Worked Answers by infinityplusone(starts at 4:49)

2019 ONE(c)