Question

Por favor, Urgente!!!
Agradeço

Answer 1

b)

f(x)=(x²-1)/(x+1)

f'(x)=[(x²-1)'*(x+1)-(x²-1)*(x+1)']/(x+1)²

f'(x)=[2x*(x+1)-(x²-1)*(1)]/(x+1)²

f'(x)=[2x²+2x-x²+1]/(x+1)²

f'(x)=[x²+2x+1]/(x+1)²

f'(x)=(x+1)²/(x+1)²

f'(x)=1

ou poderia ser assim

sabemos que x²-1=(x-1)*(x+1)

f(x)=(x²-1)/(x+1)

f(x)=(x-1)*(x+1)/(x+1)

f(x)=(x-1)

f'(x)=1

d)

f(x)=√x/(x+1)

f'(x)=[(√x)' *(x+1)-√x* (x+1)']/(x+1)²

f'(x)=[1/(2√x) *(x+1)-√x* (1)]/(x+1)²

f'(x)=[x/(2√x)+1/(2√x)-√x]/(x+1)²

f'(x)=[√x/2+1/(2√x)-√x]/(x+1)²

f'(x)=[1/(2√x)-√x/2]/(x+1)²

f'(x)=[1/(2√x)-√x/2]/(x+1)²

f'(x)=(1-x)/[(2√x)(x+1)²]