Differentiation Rules

The process of finding a derivative is called differentiation. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

Differentiation rules

The derivative of the sum, diference, product and quotient of:

$$u=u(x)\;\mathrm{and}\;v=v(x)$$

can be found as follows:

\begin{align} {(u\pm v)}'&= {(u)}'\pm {(v)}'\\ \\ {(u\times v)}'&= {u}'\times v + u \times {v}'\\ \\ {\left(\frac{u}{v}\right)}'&= \frac{{u}'\times v - u \times {v}'}{v^{2}}\\ \end{align}

Multiplication by constant

$${(c\times u)}= c \times {u}'$$

Composition of Functions

$${u\left [ v(x) \right ]}'={u}'\left [ v(x) \right ]\times {v}'(x)$$