Question

f'(x) de f(x)=2 + x / 3 - x

Answer 1

Regra do quociente:

$\boxed{\boxed{\dfrac{d}{dx}\left[\dfrac{f(x)}{g(x)}\right]=\dfrac{f'(x)g(x)-g'(x)f(x)}{[g(x)]^{2}}}}$
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$f(x)=\dfrac{2+x}{3-x}\\\\\\f'(x)=\dfrac{(3-x)\cdot\frac{d}{dx}(2+x)-(2+x)\cdot\frac{d}{dx}(3-x)}{(3-x)^{2}}\\\\\\f'(x)=\dfrac{(3-x)\cdot1-(2+x)\cdot(-1)}{(3-x)^{2}}\\\\\\f'(x)=\dfrac{3-x+(2+x)}{(3-x)^{2}}\\\\\\f'(x)=\dfrac{3-x+2+x}{(3-x)^{2}}\\\\\\\boxed{\boxed{f'(x)=\dfrac{5}{(3-x)^{2}}}}$