(Solved): Math 171 Handwritten homework 5 2] 4. Find and simplify an expression for dy/dx. Also ...

Math 171 Handwritten homework 5

2] 4. Find and simplify an expression for $dy/dx$. Also evaluate $dy/dx$ at $x=a$. a) $y={\tan }^{?1}\left(\frac{x}{x+2}\right),a=1$ b) $y=\ln \left({\cos }^{?1}(x)\right),a=\frac{1}{\sqrt{2}}$ 12] 3. Find and simplify an expression for $dy/dx$. a) $y=x^{?5}\ln (x)$ b) $y=66^{\ln (x)}?2{\log }_4\left(x^3\right)$ c) $y=(2+\sin (x){)}^{x^3}$ 8] 5. A circle is growing with time. a) At a certain moment, the circle's radius is 25 inches and is increasing at $3\mathrm{in}/\sec$. At what rate is the circle's area increasing at this same moment? b) At another moment, the circle's area is increasing at $80{\mathrm{in}}^2/\sec$ and its radius is increasing at 2 in/sec. At this moment, what is the radius of the circle? 6] 6. A particle is travelling along the elliptic path $x^2+4y^2=100$. At the moment when the particle passes through the point $(x,y)=(8,3)$, its horizontal velocity is $dx/dt=?15$ meters per second. What is the particle's vertical velocity $dy/dt$ at that same moment?