Derivative General Aef0C1
1. The problem is to find the derivative of a function, but since the function is not specified, let's explain the general process of differentiation.
2. The derivative of a function $f(x)$, denoted as $f'(x)$ or $\frac{d}{dx}f(x)$, measures the rate at which $f(x)$ changes with respect to $x$.
3. The basic rules of differentiation include:
- Power rule: $\frac{d}{dx} x^n = n x^{n-1}$
- Constant rule: $\frac{d}{dx} c = 0$ where $c$ is a constant
- Sum rule: $\frac{d}{dx} [f(x) + g(x)] = f'(x) + g'(x)$
- Product rule: $\frac{d}{dx} [f(x) g(x)] = f'(x) g(x) + f(x) g'(x)$
- Quotient rule: $\frac{d}{dx} \left( \frac{f(x)}{g(x)} \right) = \frac{f'(x) g(x) - f(x) g'(x)}{[g(x)]^2}$
- Chain rule: $\frac{d}{dx} f(g(x)) = f'(g(x)) g'(x)$
4. To find the derivative of a specific function, apply these rules step-by-step to simplify and differentiate each term.
Since no specific function was given, this is the general method to find the derivative.
Final answer: The derivative depends on the function provided; use the above rules to compute it.