Standard +0.3 This is a straightforward implicit differentiation question requiring the product rule for the middle term and chain rule for y². The point is given, so students simply substitute to find the numerical gradient. This is slightly easier than average as it's a direct application of a standard technique with no additional problem-solving required.
Obtain \(6ye^{2x}+3e^{2x}\frac{dy}{dx}\) as derivative of \(3ye^{2x}\)
B1
Allow unsimplified
Obtain \(2y\frac{dy}{dx}\) as derivative of \(y^2\)
B1
Obtain \(4\) as a derivative of \(4x\) and zero as a derivative of \(10\)
B1
Dependent B mark, must have at least one of the two previous B marks
Substitute \(0\) and \(2\) to find gradient of curve
M1
Dependent on at least one B1
Obtain \(-\frac{16}{7}\) or \(-2.29\)
A1
Allow greater accuracy
## Question 4:
| Answer | Mark | Guidance |
|--------|------|----------|
| Obtain $6ye^{2x}+3e^{2x}\frac{dy}{dx}$ as derivative of $3ye^{2x}$ | B1 | Allow unsimplified |
| Obtain $2y\frac{dy}{dx}$ as derivative of $y^2$ | B1 | |
| Obtain $4$ as a derivative of $4x$ and zero as a derivative of $10$ | B1 | Dependent B mark, must have at least one of the two previous B marks |
| Substitute $0$ and $2$ to find gradient of curve | M1 | Dependent on at least one B1 |
| Obtain $-\frac{16}{7}$ or $-2.29$ | A1 | Allow greater accuracy |
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4 Find the gradient of the curve
$$4 x + 3 y \mathrm { e } ^ { 2 x } + y ^ { 2 } = 10$$
at the point $( 0,2 )$.\\
\hfill \mbox{\textit{CAIE P2 2018 Q4 [5]}}