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 dxdf. In Lagrange notation, it is written as f′(x).
Step 1: Define the Function f(x)
We start by defining the function f(x)=x2.
Step 2: Compute the Derivative Using Leibniz Notation
Using Leibniz notation, the derivative of f(x) with respect to x is computed as:
dxdf=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)=dxd(x2)