# Rules of Differentiation for Algebraic Function

In this tutorial we discuss basic formulas of differentiation for algebraic function.

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. $\frac{d}{{dx}}{x^n} = n{x^{n - 1}}$, This is known as Power Rule of Derivative.

5. $\frac{d}{{dx}}{\left[ {f\left( x \right)} \right]^n} = n{\left[ {f\left( x \right)} \right]^{n - 1}}f'\left( x \right)$, This is called 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. $\frac{d}{{dx}}\left[ {f\left( x \right)g\left( x \right)} \right] = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + g\left( x \right)\frac{d}{{dx}}f\left( x \right)$ This is known as product rule of differentiation.

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

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