The DerivativeChapter 3

By: Hassan, JSKY, Spawz

Key ConceptsDefinition of Derivative Tangent Line Instantaneous velocity Power RuleFind Equation of a Tangent LineProduct RuleQuotient RuleChain RuleTrig Derivatives Finding 2nd Derivative

Definition

• Derivative-Studying rate at which one quantity changes relative to another. It is a tangent line of a slope.

Tangent Line

• Segment that hits one point

Ex.) Y= 4x-2

Power Rule

Equation of a Tangent Line

Given that f(-2)=4 and f’(-2)=6, find the equation of the tangent line to the graph of y=f(x) at x=-2

Instantaneous Rate of ChangeIt simply means find the derivative.

Find the instantaneous rate of change of y with respect to x at any arbitrary value for x using the definition.

y=4x-2

Product Rule

f(x)=(3 -6)(2x-3)

Quotient Rule

Chain Rule

y=tan

2nd Derivative

• Find the derivative of the first derivative

y=sin(3x)

Trig Derivatives