Sunny

Was ist die Ableitung von `arctan (x / 2)`? Antworten: `2/(4+x^2)` Erläuterung: differentiate using the `color(blue)“chain rule“` `color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))…….. (A)` Note that `x/2=1/2x` let `color(blue)(u=1/2x)rArr(du)/(dx)=1/2` `color(orange)“Reminder“ color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(arctanx)=1/(1+x^2))color(white)(a/a)|)))` and `y=arctancolor(blue)(u)rArr(dy)/(du)=1/(1+color(blue)(u)^2` Substitute these values into (A) and convert u back into terms of x. `dy/dx=1/(1+(x/2)^2)xx1/2=(1/2)/((1+x^2/4))=(1/2)/(1/4(4+x^2))` `rArrdy/dx=2/(4+x^2)`