Questions: Conceptual: A. Write two different notations to express the derivative of function f(x).

Solution Steps

To express the derivative of a function $f(x)$, we can use two different notations: the Leibniz notation and the Lagrange notation. In Leibniz notation, the derivative is written as $\frac{df}{dx}$. In Lagrange notation, it is written as $f'(x)$.

We start by defining the function $f(x) = x^2$.

Using Leibniz notation, the derivative of $f(x)$ with respect to $x$ is computed as: $$\frac{df}{dx} = 2x$$

Using Lagrange notation, the derivative of $f(x)$ with respect to $x$ is expressed as: $$f'(x) = \frac{d}{dx}(x^2)$$

Final Answer