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.