5 Important Patterns of First Principles

First Principles

The First Principles defines how basic rule of derivative of a function.
$$\displaystyle f'(x) = \lim_{h\to\infty} \frac{f(x+h)-f(x)}{h}$$

Patterns of the First Principles

Pattern 1

Differentiate \( f(x) = x^2 \) from the first principles.

Pattern 2

Differentiate \( f(x) = x^3 \) from the first principles.

Pattern 3

Differentiate \( f(x) = \sqrt{x} \) from the first principles.

Pattern 4

Differentiate \( \displaystyle f(x) = \frac{1}{x} \) from the first principles.

Pattern 5

Differentiate \( \displaystyle f(x) = \sqrt[3]{x} \) from the first principles.