Question

Sa se calculeze f '(x) unde:
a)f(x)=(x+2)$e^{x}$
b)f(x)=$\frac{3}{x}$+lnx-x+1
c)f(x)=$\frac{x+3}{x^{2} +2}$

Answer 1

Răspuns:

a) f `(x)=(x+2) `*eˣ+(x+2)*eˣ`=eˣ+(x+2)eˣ=eˣ(1+x+2)=eˣ(x+3)

b) f `(x)= (3/x) `+lm `x +1 `= -3/x²+1/x+0 =-3/x²+1/x

c) f `(x)=[(x+3 )`(x²+2)-(x+3)(x²+2) `]/(x²+2)²=

(x²+2-2x(x+3)/(x²+2)²=(x²+2-2x²-6x)/(x²+2)²=

(-x²-6x+2)/(x²+2)²

Explicație pas cu pas: