Function

Derivative

c (constant)

0

x

1

c∙x

c

x^{c}

c∙x^{c1}

x^{n}

n∙x^{n1}

x^{1}=1/x

x^{2}

x^{c}=1/x^{c}

c∙x^{c1}

x^{1/2}=√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/x^{2}
y =  8/x^{2}=  8 x ^{2} = 8 – 2 * x^{21} = 16 x^{3}
Example 3: Evaluate the derivative of √ (32)^{√ 2}
Example 4: Calculate the derivative of