# Rules of Differentiation for Algebraic Functions

In this tutorial we will discuss the basic formulas of differentiation for algebraic functions.

**1.** $$\frac{d}{{dx}}\left( c \right) = 0$$, where $$c$$ is any constant.

**2.** $$\frac{d}{{dx}}\left( x \right) = 1$$.

**3.** $$\frac{d}{{dx}}\left( {cx} \right) = c$$, where $$c$$ is any constant.

**4.** $$\frac{d}{{dx}}{x^n} = n{x^{n – 1}}$$, which is known as the power rule of a derivative.

**5.** $$\frac{d}{{dx}}{\left[ {f\left( x \right)} \right]^n} = n{\left[ {f\left( x \right)} \right]^{n – 1}}f’\left( x \right)$$, which is called the general power rule.

**6.** $$\frac{d}{{dx}}\left[ {f\left( x \right) + g\left( x \right)} \right] = \frac{d}{{dx}}f\left( x \right) + \frac{d}{{dx}}g\left( x \right)$$

**7.** $$\frac{d}{{dx}}\left[ {f\left( x \right) – g\left( x \right)} \right] = \frac{d}{{dx}}f\left( x \right) – \frac{d}{{dx}}g\left( x \right)$$

**8.** $$\frac{d}{{dx}}\left[ {f\left( x \right)g\left( x \right)} \right] = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + g\left( x \right)\frac{d}{{dx}}f\left( x \right)$$ which is known as the product rule of differentiation.

**9.** $$\frac{d}{{dx}}\left[ {\frac{{f\left( x \right)}}{{g\left( x \right)}}} \right] = \frac{{g\left( x \right)\frac{d}{{dx}}f\left( x \right) – f\left( x \right)\frac{d}{{dx}}g\left( x \right)}}{{{{\left[ {g\left( x \right)} \right]}^2}}}$$ which is known as the quotient rule of differentiation.

**10.** $$\frac{d}{{dx}}\left[ {\left( {f \circ g} \right)\left( x \right)} \right] = f’\left[ {g\left( x \right)} \right]g’\left( x \right)$$ which is known as the chain rule of differentiation.