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 $\frac{dy}{dx} = 4\pi x^{\pi - 1}$