The equation of a curve is $e^y = \sqrt{1 - 2x^2}$. Obtain an expression for \(\frac{\mathrm{

Question

The equation of a curve is $e^y = \sqrt{1 - 2x^2}$. Obtain an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$. The point $P$ moves along the curve such that its $y$-coordinate is decreasing at a constant rate of $2$ units/s. Explain whether a real point $P$ can have $x=2$, and hence whether the requested rate at that value can exist.

Accepted Answer

(i) $\dfrac{\mathrm{d}y}{\mathrm{d}x}=-\dfrac{2x}{1-2x^2}$ (ii) No real value: $x=2$ is outside the curve's domain

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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