Basic Differentiation Rules Rates of Change. The Constant Rule The derivative of a constant function is 0. Why?

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Presentation transcript:

Basic Differentiation Rules Rates of Change

The Constant Rule The derivative of a constant function is 0. Why?

The Power Rule Remember that the derivative is just the slope of a tangent line.

The Power Rule Remember d/dx [x] = 1 because the slope of y = x is 1

Finding an Equation of a Tangent Line First find the slope of the tangent line (derivative) Next substitute the given value in for x (this is the slope) Use y = mx +b to find the y-intercept Finally write the equation in y = mx + b form

Constant Multiple Rule If f is a differentiable function and c is a real number, then cf is also differentiable and

Sum and Difference Rules The derivative of the sum (or difference) of two differentiable functions is differentiable and is the sum (or difference) of their derivatives.

Derivatives of Sine and Cosine Functions

Rates of Change Finding Average Velocity of a Falling ObjectAverage Velocity Finding Instantaneous Velocity of a Falling ObjectInstantaneous Velocity