What is differentiation in simple words? (2024)

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Integration as Antiderivative

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Solution

Differentiation
Differentiation is the process of finding the derivative of a function.
It can also be defined as the process of finding the rate of change of a function with respect to its variables.
It is usually denoted as $\frac{d y}{d x}$ , where $y = f (x)$
Some of the basic rules of derivation are:
The derivative of a constant is zero.
Power rule: $\frac{d}{d x} (x^{n}) = n x^{n - 1}$
Multiplication constant: $\frac{d}{d x} [c f (x)] = c \cdot \frac{d}{d x} f (x)$
Sum rule: $\frac{d}{d x} [f (x) + g (x)] = \frac{d}{d x} f (x) + \frac{d}{d x} g (x)$
Difference rule: $\frac{d}{d x} [f (x) - g (x)] = \frac{d}{d x} f (x) - \frac{d}{d x} g (x)$
Product rule: $\frac{d}{d x} [f (x) \cdot g (x)] = [f (x) \cdot \frac{d}{d x} g (x)] + [g (x) \cdot \frac{d}{d x} f (x)]$
Quotient rule: $\frac{d}{d x} [\frac{f (x)}{g (x)}] = \frac{[g (x) \cdot \frac{d}{d x} f (x)] - [f (x) \cdot \frac{d}{d x} g (x)]}{{[g (x)]}^{2}}$

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