Understanding Differentiation
Differentiation is the process of finding the derivative of a function, which measures how a function value changes as its input changes. This is a fundamental concept in calculus and essential in numerous scientific and engineering applications. 🚀
Why Differentiation?
- To find rates of change.
- To solve problems involving motion.
- To optimize solutions (finding maxima and minima).
Basic Differentiation Formulas
Here are some key formulas to get you started:
- The derivative of a constant is zero.
- The power rule: \( f(x) = x^n \Rightarrow f'(x) = nx^{n-1} \)
- The constant multiple rule: \( f(x) = c \cdot g(x) \Rightarrow f'(x) = c \cdot g'(x) \)
- The sum rule: \( f(x) = g(x) + h(x) \Rightarrow f'(x) = g'(x) + h'(x) \)
