Qual è la derivata di cosx ^ 2 cosx2?
Risposta:
-sin2x−sin2x
Spiegazione:
Differentiate using the color(blue)"chain rule"chain rule
color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x))g'(x))color(white)(a/a)|))) ........ (A)
color(orange)"Reminder"
color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(cosx)=-sinx)color(white)(a/a)|)))
color(blue)"-----------------------------------------------"f(g(x))=cos^2x=(cosx)^2rArrf'(g(x))=2(cosx)^1=2cosx
and g(x)=cosxrArrg'(x)=-sinx
color(blue)"-----------------------------------------------"
Substitute these values into (A)rArrf'(g(x))=2cosx(-sinx)=-2sinxcosx
Using the following trig. identity to simplify.
color(orange)"Reminder"
color(red)(|bar(ul(color(white)(a/a)color(black)(sin2x=2sinxcosx)color(white)(a/a)|)))
rarrf'(g(x))=-2sinxcosx=-sin2x