Subjects calculus

Derivative 07C2F0

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Derivative 07C2F0


1. The problem is to find the derivative of a function, but the function is not specified. 2. The derivative of a function $f(x)$, denoted $f'(x)$ or $\frac{d}{dx}f(x)$, measures the rate at which $f(x)$ changes with respect to $x$. 3. Common rules for derivatives 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: $\frac{d}{dx} f(g(x)) = f'(g(x)) g'(x)$ Since the function is not given, please provide the function to differentiate for a specific solution.