The equation of a curve is such that $e^{2y} = 7x^4 + 2$. Obtain an expression for \(\fr

Question

The equation of a curve is such that $e^{2y} = 7x^4 + 2$. 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 $\frac{2}{3}$ unit/s. Find the rate of change of the $x$-coordinate $P$ when $x = 1$.

Accepted Answer

(i) $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{14x^3}{7x^4+2}$ (ii) $-\dfrac37\text{ unit s}^{-1}$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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