|||| 14.5 The Chain Rule

Mar 15, 2019

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ITK-122 Calculus II. |||| 14.5 The Chain Rule. Dicky Dermawan www.dickydermawan.net78.net dickydermawan@gmail.com. |||| 14.5 The Chain Rule. |||| 14.5 The Chain Rule. |||| 14.5 The Chain Rule. |||| 14.5 The Chain Rule. Implicit Differentiation. }. Implicit Differentiation.

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|||| 14.5 The Chain Rule

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ITK-122 Calculus II |||| 14.5 The Chain Rule DickyDermawan www.dickydermawan.net78.net dickydermawan@gmail.com
|||| 14.5 The Chain Rule
|||| 14.5 The Chain Rule
|||| 14.5 The Chain Rule
|||| 14.5 The Chain Rule
Implicit Differentiation • }
Implicit Differentiation

Chain Rule

Chain Rule. If f and g are differentiable, then so is their composition f(g(x)) Resulting differentiation formula called chain rule. First Approach. Examples. Compute the derivatives of the following functions:. Remark.

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Chain Rule :

Chain Rule :. Used to find the derivative of a composite function. Chain Rule :. Used to find the derivative of a composite function. Chain Rule :. Used to find the derivative of a composite function. Chain Rule :. Used to find the derivative of a composite function. Chain Rule :.

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2.4 The Chain Rule

2.4 The Chain Rule. "I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives. -- Charles Hermite . Objectives:. To find derivatives using the chain rule. Two ways. Find the derivative of . A third way…. Chain rule

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The Chain Rule

The Chain Rule. Wednesday, Feb. Velocity & Acceleration. Velocity = slope of a displacement-time graph Acceleration = slope of a velocity-time graph. Velocity & Acceleration. If the velocity is positive, The object is moving forward

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The Chain Rule

The Chain Rule. Section 3.6c. Suppose that functions f and g and their derivatives have the f ollowing values at x = 2 and x = 3. 2. 8. 2. 1/3. –3. 3. 3. –4. 5. Evaluate the derivatives with respect to x of the following c ombinations at the given value of x . (a).

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The Chain Rule

The Chain Rule. By Dr. Julia Arnold. Rule 7: The Chain Rule. If h(x) = g(f(x)), then h’(x) = g’(f(x))f’(x). The Chain Rule deals with the idea of composite functions and it is helpful to think about an outside and an inside function when using The Chain Rule.

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The Chain Rule

The Chain Rule. Working on the Chain Rule. Review of Derivative Rules. Using Limits:. Power Rule. If f(x) =. Product Rule. Quotient Rule. Why use the chain rule?. The previous rules work well to take derivatives of functions such as

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3.6 The Chain Rule

3.6 The Chain Rule. We know how to differentiate sinx and x ² - 4, but how do we differentiate a composite like sin (x² - 4)? The answer is the Chain Rule. The Chain Rule is probably the most widely used differentiation rule in mathematics. Relating Derivatives.

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CHAIN RULE

CHAIN RULE. How to differentiate composite function. The differentiation formulas you learned by now do not enable you to calculate F ’( x ). It turns out that the derivative of the composite function f ◦ g is the product of the derivatives of f and g .

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The Chain Rule

The Chain Rule. Objective. To use the chain rule for differentiation. The Chain Rule. The Chain Rule is a technique for differentiating composite functions . Composite functions are made up of layers of functions inside of functions. The Chain Rule. The outside. The Chain Rule.

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Chain Rule

Chain Rule. 3.5. Consider:. These can all be thought of as composite functions F(g(x)). Derivatives of Composite functions are found using the chain rule. The Chain Rule. Consider the composition of two functions f ( x ) and g ( x ) given by

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Chain Rule

Chain Rule. and Trig. What is to be learned?. How to apply the chain rule to trig functions. Type 1. y = sin(3x + 10). , where U = 3x + 10. let y = sin U. dy / du. du / dx. = 3. = cos U. = Cos U. dy / dx. 3. = 3Cos U. = 3Cos(3x + 10). The Chain Rule. Type sin (ax + b).

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The Chain Rule

The Chain Rule. Gottfried Wilhelm von Leibniz 1646 - 1716.

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The Chain Rule

The Chain Rule. What is to be learned?. How to differentiate a composite function. f(x) = (x + 5) 2. = x 2 + 10x + 25. . f(x) = (x + 5) 7. . y = (2x + 5) 7. remember sin( 2x + 30 ) = 0.8. dy / dx. where A = 2x + 30. sinA = 0.8,. let y= u 7. where u = 2x + 5. dy / du. = 7u 6.

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The Chain Rule

The Chain Rule. The Problem. Complex Functions Why?  not all derivatives can be found through the use of the power, product, and quotient rules. Working To A Solution. Composite function f(g(x))  f is the outside function, g is the inside function z=g(x), y=f(z), and y=f(g(x))

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The Chain Rule

The Chain Rule. By: Bryan Porter Caleb Clark Matt Devries. The Chain Rule. Involves taking the derivative of a function with a different function inside of it To solve you need to: Take the derivative of the outside Leave the inside alone Multiply it with the derivative of the inside

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The Chain Rule

The Chain Rule. Section 3.5. The Chain Rule. According to Mrs. Armstrong … “Pull the chain and the light comes on!”. Introduction. Sludge Falls CO 2 is changing at rate of 0.02 ppm for each person Population growing at rate of 1000 people/yr

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The Chain Rule

The Chain Rule. Section 2.4. After this lesson, you should be able to:. Find the derivative of a composite function using the Chain Rule. Find the derivative of a function using the General Power Rule. Simplify the derivative using algebra.

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The Chain Rule

The Chain Rule. Chapter 3.4. The Chain Rule. The Chain Rule might perhaps be the most important of the differentiation rules It tells us how to differentiation a function within a function That is, it tells us how to differentiate a composition of functions

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2.4 The Chain Rule

2.4 The Chain Rule. Remember the composition of two functions?. The chain rule is used when you have the composition of two functions. f(x) = x 3. Find y’ for y = (x 2 + 1) 3. g(x) = x 2 + 1. y’ = 3(x 2 + 1) 2. = 6x(x 2 + 1) 2. (2x). Find y’ for y = (3x – 2x 2 ) 3.

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Differentiating The Chain Rule

Differentiating The Chain Rule. e.g. 1 Find if. We need to recognise the function as and identify the inner function ( which is u ). Solution:. Let. Then. Differentiating:. We don’t multiply out the brackets.

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The Chain Rule

The Chain Rule. Mr. Miehl miehlm@tesd.net. Objective. To use the chain rule for differentiation. The Chain Rule. The Chain Rule is a technique for differentiating composite functions . Composite functions are made up of layers of functions inside of functions. The Chain Rule.

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