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Derivatives of Simple Functions

Function

Derivative

c (constant)

0

x

1

c∙x

c

xc

c∙xc-1

xn

n∙xn-1

x-1=1/x

-x-2

x-c=1/xc

-c∙x-c-1

x1/2=√x

1/(2√x), where x>0

 

 

Example 1: Find the derivative of the function f(x) = Pi (3 + √ 5).

This function is simply a constant equal to approximately 5.2, thus it’s derivative is 0

 

Example 2: Find the derivative of y = - 8/x2

 

y = - 8/x2= - 8 x -2 = -8 – 2 * x-2-1 = 16 x-3

 

Example 3: Evaluate the derivative of √ (32)√ 2 




Example 4: Calculate the derivative of 
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