1.7.19 Parametric and implicit differentiation (A-level only)

A magnetic field is modeled such that a specific field line $C$ follows the equation

5y^{2} + 2xy^{2} = 10(5^{x}) + 10, \quad y > 0

where $x$ and $y$ are distances in centimeters.

Determine an expression for $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[6]

The field line $C$ crosses the $y$ -axis at the point $P$ .

Find the exact value of the gradient of the field line at $P$ .

[4]

1.7.19 Parametric and implicit differentiation (A-level only) Questions

A magnetic field is modeled such that a specific field line $C$ follows the equation

5y^{2} + 2xy^{2} = 10(5^{x}) + 10, \quad y > 0

where $x$ and $y$ are distances in centimeters.

Determine an expression for $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[6]

The field line $C$ crosses the $y$ -axis at the point $P$ .

Find the exact value of the gradient of the field line at $P$ .

[4]