Answer to Question #280256 in Calculus for Alibaba

Question

If y=sin(2x)/x and x =Pi and ex=.25 find the differentaite

Answer 1

Solution;

Given;

x=π

$e^x=0.25$

$y=\frac{sin(2x)}{x}$

$ln(e^x)=ln(0.25)$

$x=ln(0.25)$

Apply quotient rule;

$\frac{dy}{dx}=\frac{2xcos(2x)-sin(2x)}{x^2}$

At x=π;

$\frac{dy}{dx}=\frac{2πcos(2π)-sin(2π)}{π^2}$ =$\frac{2π-0}{π^2}=\frac2π$

At x=ln(0.25)

$\frac{dy}{dx}=\frac{2ln0.25cos(2×ln0.25)-sin(2×ln0.25)}{(ln0.25)^2}$

$\frac{dy}{dx}=-1.415$