BASIC DIFFERENTIATION RULES AND RATES OF CHANGE Section
BASIC DIFFERENTIATION RULES AND RATES OF CHANGE Section 2. 2
When you are done with your homework, you should be able to… • Find the derivative of a function using the Constant Rule • Find the derivative of a function using the Power Rule • Find the derivative of a function using the Constant Multiple Rule • Find the derivative of a function using the Sum and Difference Rules • Find the derivatives of the sine function and the cosine function • Use derivatives to find rates of change
THE CONSTANT RULE The derivative of a constant function is zero. That is, if c is a real number, then
Find the slope of A. -3 B. 0 C. undefined
A. B. C. D. -3 0 undefined ?
THE POWER RULE If n is a rational number, then the function is differentiable and For f to be differentiable at n must be a number such that is defined on an interval containing 0.
Evaluate A. B. C. D.
Evaluate A. B. C. D. Both A and B
THE CONSTANT MULTIPLE RULE If f is a differentiable function and c is a real number, then cf is also differentiable and
Evaluate A. B. C. D.
Evaluate the derivative of at A. B. C. D. 81 -162 -810 -486
THE SUM AND DIFFERENCE RULES • The sum or difference of two differentiable functions f and g is itself differentiable. – The derivative of the sum or difference of functions is the sum or difference of the derivatives of f and g.
DERIVATIVES OF SINE AND COSINE FUNCTIONS
Evaluate the slope of the graph at A. 1/2 B. C. -1/2 D.
RATES OF CHANGE • Velocity – Average Velocity – Instantaneous Velocity
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