Question

Derivada de y em relação a x:
a) tg(x+y)=4

Answer 1

$[tg(u)]' sec^2 (u) *u'\\\\\\ tg(x+y)= 4\\\\ \frac{d}{dx}[tg(x+y)]= \frac{d}{dx} (4)\\\\ sec^2(x+y)* \frac{d}{dx}(x+y) = 0\\\\ \frac{d}{dx}(x+y)=0\\\\ \frac{d}{dx}(x)+ \frac{d}{dx}(y) = 0\\\\ 1+ \frac{dy}{dx}=0\\\\\boxed{\boxed{ \frac{dy}{dx} =-1}}$