Garland

Qual é a derivada de `cosx ^ 2`? Responda: `-sin2x` Explicação: Differentiate using the `color(blue)”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`