Question

Y=e^x-0.3x^2 производная функция

Answer 1

У'=(е^х-0,3х^2)'=е^х-0,3*2х^(2-1)=е^х-0,6х

Answer 2

To find the derivative of the function $Y = e^x - 0.3x^2$ with respect to $x$, we can use the rules of differentiation. The derivative of a function represents the rate at which the function is changing with respect to its independent variable, $x$.

The general rules for differentiating common functions are as follows:

1. The derivative of $e^x$ is $e^x$.
2. The derivative of $x^n$ (where $n$ is a constant) is $nx^{(n-1)}$.

Using these rules, we can differentiate the given function:

\frac{dY}{dx} &= \frac{d}{dx}(e^x - 0.3x^2) \\ &= \frac{d}{dx}(e^x) - \frac{d}{dx}(0.3x^2) \\ &= e^x - 0.3 \cdot \frac{d}{dx}(x^2) \\ &= e^x - 0.3 \cdot 2x \\ &= e^x - 0.6x \end{align*} \] So, the derivative of the function \(Y = e^x - 0.3x^2\) with respect to \(x\) is \(e^x - 0.6x\).