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DIFFERENTIATION & INTEGRATION CHAPTER 4

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Differentiation is the process of finding the derivative of a function. Derivative of INTRODUCTION TO DIFFERENTIATION

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Derivative of a Power Function Theorem 1 Derivative of a Constant Times a Function TECHNIQUES OF DIFFERENTIATION

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Derivative of Sum and Difference Rules

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Example :

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Derivative of a Product

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Example : Differentiate

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Derivative of Quotient

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Example : Differentiate

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EXERCISE 1

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Derivative of Trigonometric Functions

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Example : Differentiate :

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Derivative of Exponential and Logarithmic Functions

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Example :

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The Chain Rule Example :

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EXERCISE 2

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Implicit Differentiation Implicit differentiation is the process of taking the derivative when y is defined implicitly or in y is a function of x. Example :

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EXERCISE 3

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A parametric derivative is a technique for finding derivative when both x and y variables depend on an independent third variable, t (time). PARAMETRIC DIFFERENTIATION

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Example : Solve for if:

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Consider y =f(x) with point for function of a graph. Tangent line – straight line that touches y = f(x). Normal line – line that is perpendicular to tangent line. Slope of tangent line, Equation of the line tangent Equation of normal line TANGENT AND NORMAL LINE

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Example : Given a curve equation at point (2,-1). a)Implicitly differentiate the equation.

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b) Find the equation of the line tangent of the curve. Step 1 : Find the slope of tangent, m. Step 2 : Find the equation using

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c) Find the equation of the normal line of the curve.

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1.If, find the equation of the tangent line at (-1,4). 2.If, find the slope of the tangent line to the curve where. Find the equation of the line tangent to the curve where EXERCISE 4

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