Question

Qual é a derivada de Y?

Answer 1

$\displaystyle y=\frac{2x-1}{e^x} \\ \\ \\ y' = \frac{(2x-1)' \cdot e^x - (2x-1) \cdot e^x'}{(e^x)^2} \\ \\ \\ y' = \frac{2e^x-(2e^{x} x - e^x)}{e^{2x}} \\ \\ \\ y' = \frac{2e^x-2e^{x} x + e^x}{e^{2x}} \\ \\ \\ y' = \frac{3e^x-2e^x x}{e^{2x}} \\ \\ \\ y' = \frac{e^x \cdot (3-2x)}{e^{2x}} \\ \\ \\ y' = \frac{3-2x}{e^x} \\ \\ \\ f(0) = \frac{3-2 \cdot 0}{e^0} \\ \\ \\ \boxed{\boxed{f(0) = 3 }}$