To differentiate \( f(x) = \frac{x^{5}}{2} \) using the first principles (also known as the definition of a derivative), we follow these steps:

### Step 1: Definition of the derivative
The derivative of a function \( f(x) \) at a point \( x \) is defined as:

\[
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
\]

For \( f(x) = \frac{x^5}{2} \), we will apply this definition.

### Step 2: Substitute \( f(x) = \frac{x^5}{2}

Learn how to differentiate the function x^5/2 using the first principles of calculus. This step-by-step solution explains the core concepts of differentiation and the definition of a derivative, ideal for students in Grades 11-12.

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