Given that $y=\frac{x+5}{\sqrt{2x+5}}$, show that $\frac{\mathrm{d}y}{\mathrm{d}x}$ can be writt

Question

Given that $y=\frac{x+5}{\sqrt{2x+5}}$, show that $\frac{\mathrm{d}y}{\mathrm{d}x}$ can be written in form $\frac{kx}{\sqrt{(2x+5)^3}}$ find the rate of change of $x$ when $x=10$, if $y$ is decreasing at the rate of $2$ units per second at this instant.

Accepted Answer

(a) $k=1$ (b) $\frac{\mathrm dx}{\mathrm dt}=-25\text{ units s}^{-1}$

Techniques of Differentiation - Quotient Rule

Techniques of Differentiation - Quotient Rule

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