The equation of a curve is $ y = \frac{2 \ln x}{x} . $ Obtain an expression for \(\frac{\math

Question

The equation of a curve is $ y = \frac{2 \ln x}{x} . $ Obtain an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$. The point $P$ moves along the curve such that its $x$-coordinate is increasing at a constant rate of $0.03$ unit/s. Find the rate of change of the $y$-coordinate of $P$ when $x = 1$.

Accepted Answer

(i) $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{2(1-\ln x)}{x^2}$ (ii) $0.06\text{ unit s}^{-1}$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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