Differentiation Rules

Differentiation Rules

Constant Rule

• If y = c or f(x) = c, where c is a constant, then \frac{dy}{dx} = 0 or f'(x) = 0.

  • Example:

    1. If y = 3, then \frac{dy}{dx} = 0.
    2. If y = \frac{2}{5}, then \frac{dy}{dx} = 0.
    3. If y = \sqrt{3}, then \frac{dy}{dx} = 0.
    4. If y = \pi, then \frac{dy}{dx} = 0.

Power Rule

• If y = ax^n, where a and n are constants, then \frac{dy}{dx} = n \cdot a x^{n-1} or f'(x) = n \cdot a x^{n-1}.

  • Note:

    • If y = x, then \frac{dy}{dx} = 1.
    • If y = ax, then \frac{dy}{dx} = a.

  • Example:

    1. If y = x, then \frac{dy}{dx} = 1.
    2. If y = 5x, then \frac{dy}{dx} = 5.
    3. If y = \frac{1}{4}x^4, then \frac{dy}{dx} = x^3.
    4. If y = 4x^{\pi}, then \frac{dy}{dx} = 4\pi x^{\pi - 1}