# Find Derivatives of Functions in Calculus

Find the derivatives of various functions using different methods and rules. Several Examples with detailed solutions are presented. More exercises with answers are at the end of this page.

** Example 1:** Find the derivative of function f given by

__Solution to Example 1:__

- Function f is the product of two functions: U = x 2 - 5 and V = x 3 -2x+3. We use the product rule to differentiate f as follows:

** Example 2:** Calculate the first derivative of function f given by

__Solution to Example 2:__

- This function may be considered as the product of function U = sqrt x + 2x and V = 4x 2 - 1, hence the use of the product rule

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and group to obtain the final result for the derivative of f as follows.** Example 3:** Calculate the first derivative of function f given by

__Solution to Example 3:__

- The given function may be considered as the ratio of two functions: U = x 2 + 1 and V = 5x - 3 and use the quotient rule to differentiate f is used as follows

** Example 4:** Calculate the first derivative of function f given by

__Solution to Example 4:__

- Function f is the quotient of two functions hence the use of the quotient rule

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