Subjects calculus

Differentiation Basics

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Differentiation Basics


1. The problem is to understand the concept of differentiation in calculus. 2. Differentiation is the process of finding the derivative of a function, which represents the rate of change of the function with respect to a variable. 3. For example, if we have a function $f(x) = x^2$, the derivative $f'(x)$ is found by applying the power rule: $$f'(x) = 2x$$ 4. This means the slope of the function $x^2$ at any point $x$ is $2x$. 5. Differentiation rules include the power rule, product rule, quotient rule, and chain rule, which help find derivatives of more complex functions. 6. Understanding differentiation is fundamental in fields like physics, engineering, and economics for analyzing change and motion.