3.3 Differentiation Rules

Find the derivative of g(x) = (1)/x^7) using the extended power rule

-7x^-8

Find the derivative of g(x) = -3

0 use the constant rule

Example: Finding the Derivative of a Function using the Power Rule Find the derivative of the function f(x) = x^10 using the power rule

10x^9

Use the product rule to obtain the derivative of j(x) = 2x^5(4x²+x)

56x^6 + 12x^5

Find the derivative of f(x) = 2x³-6x²+3

6x²-12x

Power Rule for Derivatives

Be aware that this rule doesn't apply to functions in which a constant is raised to a variable power, such as f(x) = 3^x

Constant Rule for Derivatives

If f(x)=b, where b is a constant, then f'(x)=0

Find the equation of the line tangent to the graph of f(x) = 3x²-11, at x = 2

y=12x-23

Find the derivative of h(x) = (3x+1)/(4x-3) *using the quotient rule*

h'(x) = - (13)/(4x-3)²