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

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

Solution

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) $.

Step 1: Define the Function $ f(x) $

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

Step 2: Compute the Derivative Using Leibniz Notation

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

Step 3: Compute the Derivative Using Lagrange Notation

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