Câu 1:
$f(x)=\dfrac{1}{x+2}\to f'(x)=\dfrac{(x+2)'}{2\sqrt{x+2}}=\dfrac{1}{2\sqrt{x+2}}$
$\to P=f(2)+( x+2)f'(2)=\sqrt{2+2}+(x+2).\dfrac{1}{2\sqrt{2+2}}=\dfrac{1}{4}x+\dfrac{5}{2}$
Câu 2:
$f(x)=\dfrac{1}{x^3+1}\to f'(x)=-\dfrac{(x^3+1)'}{(x^3+1)^2}=-\dfrac{3x^2}{(x^3+1)^2}$
$\to f'(1)=-\dfrac{3}{(1+1)^2}=\dfrac{-3}{4}$