Differentiation Rules

Differentiation Rules are rules used to compute the derivative of a function in calculus.

Basic Rules

Derivative of a Constant: If $y=c$ and c is any constant then $\frac{dy}{dx} = 0$

Sum Rule: If $y(x) = u(x)+v(x)$ then $\frac{dy}{dx} = \frac{du}{dx} + \frac{dv}{dx}$

Product Rule: If $y(x) = u(x) * v(x)$ then $\frac{dy}{dx} = u(x)\frac{dv}{dx} + v(x)\frac{du}{dx}$

Quotient Rule: If $y(X) = \frac{u(x)}{v(x)}$ then $\frac{dy}{dx} = \frac{v(x)\frac{du}{dx} - u(x)\frac{dv}{dx}}{(v(x))^2}$

Chain Rule: If $y(x) = u(v(x))$ then $\frac{dy}{dx} = \frac{du}{dv}*\frac{dv}{dx}$

power Rule: If $y(x) = u(x^n)$ then $\frac{dy}{dx} = n(u(x))^{n-1} * \frac{du}{dx}$