# 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.