Question

Sa se calculeze derivatele funcțiilor : f(x)=xe la x , f(x)=e la x sin x , f(x)=x la a 2 ctgx , f(x)= e la x (x-lnx)

Answer 1

f(x)=xeˣ
f(x)'=(xeˣ)'=(x)'eˣ+x(eˣ)'=1×eˣ+x(eˣ)=eˣ(1+x)

f(x)=eˣsin x=( eˣ)'sinx+eˣ(sinx)'=eˣsinx+eˣcos=eˣ(sin x+cos x)

f(x)=x²ctg x=(x²)'ctg x+x²(ctg x)'=2x ctgx - x²/sin²x

(ctg x)'= -1/(sin² x)