Question

The rate of change of $\sqrt{x^{2}+16}$ with respect to $\frac{x}{x-1}$ at $x=5$ is

• A. $\frac{-80}{\sqrt{41$
• B. $\frac{80}{\sqrt{41$
• C. $\frac{12}{5}$
• D. $\frac{-12}{5}$

Hint:

Logic Tip: When calculating derivative ratios at a specific point, it is usually faster to substitute the value of $x$ directly into $dy/dx$ and $dz/dx$ separately, then divide the resulting numerical values, rather than simplifying the full algebraic expression first!

Answer 1

The Correct Option is A