Question

Derivada exponencial de y=80e^(0.05x^2 )

Answer 1

y=80e^(0.05x²)

derivada exponencial es:

e^u = u' e^u         u' = u prima

.......................................................

entonces:

y=80e^(0.05x²)
y' = 80(0.05(2x)) e^(0.05x²)
y' = 80(0.1x) e^(0.05x²)
y' = 8x e^(0.05x²)

Answer 2

$y=80e^{0.05x^2}\\ \\ \frac{dy}{dx}= \frac{d}{dx}(80e^{0.05x^2} )\\ \\ \Rightarrow \frac{dy}{dx}= 80 \times \frac{d}{dx}(e^{0.05x^2} )\\ \\ \Rightarrow \frac{dy}{dx}= 80 \times (e^{0.05x^2} ) \times \frac{d}{dx}(0.05x^2) \\ \\ \Rightarrow \frac{dy}{dx}= 80 \times (e^{0.05x^2} ) \times ( 0.05 \times 2x)\\ \\ \Rightarrow \frac{dy}{dx}= \boxed{8xe^{0.05x^2}}$