91Ó°ÊÓ

, find dy/dx by logarithmic differentiation. $$ y=\frac{x+11}{\sqrt{x^{3}-4}} $$

Express the indicated derivative in terms of the function \(F(x) .\) Assume that \(F\) is differentiable. $$ \frac{d}{d x} F(\cos x) $$

Express the indicated derivative in terms of the function \(F(x) .\) Assume that \(F\) is differentiable. $$ \frac{d}{d x} \cos F(x) $$

First find and simplify $$\frac{\Delta y}{\Delta x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}$$ Then find \(d y / d x\) by taking the limit of your answer as \(\Delta x \rightarrow 0 .\) $$ y=1+\frac{1}{x} $$

, find dy/dx by logarithmic differentiation. $$ y=\left(x^{2}+3 x\right)(x-2)\left(x^{2}+1\right) $$

Express the indicated derivative in terms of the function \(F(x) .\) Assume that \(F\) is differentiable. $$ D_{x} \tan F(2 x) $$

First find and simplify $$\frac{\Delta y}{\Delta x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}$$ Then find \(d y / d x\) by taking the limit of your answer as \(\Delta x \rightarrow 0 .\) $$ y=\frac{x-1}{x+1} $$

, find dy/dx by logarithmic differentiation. $$ y=\frac{\sqrt{x+13}}{(x-4) \sqrt[3]{2 x+1}} $$

The height \(s\) in feet of a ball above the ground at \(t\) seconds is given by \(s=-16 t^{2}+40 t+100\). (a) What is its instantaneous velocity at \(t=2\) ? (b) When is its instantaneous velocity 0 ?

First find and simplify $$\frac{\Delta y}{\Delta x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}$$ Then find \(d y / d x\) by taking the limit of your answer as \(\Delta x \rightarrow 0 .\) $$ y=\frac{x^{2}-1}{x} $$