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

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 $f(x)$.
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Solution

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Solution Steps

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

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

We start by defining the function f(x)=x2 f(x) = x^2 .

Step 2: Compute the Derivative Using Leibniz Notation

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

Step 3: Compute the Derivative Using Lagrange Notation

Using Lagrange notation, the derivative of f(x) f(x) with respect to x x is expressed as: f(x)=ddx(x2) f'(x) = \frac{d}{dx}(x^2)

Final Answer

dfdx=2x and f(x)=2x\boxed{\frac{df}{dx} = 2x \text{ and } f'(x) = 2x}

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