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b) Now, start with the exact same equation as before, i.e. Vz+ Vj= 5,

b) Now, start with the exact same equation as before, i.e. Vz+ Vj= 5,

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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Question 4a
4. Now, as explained in class, recall that some functions are defined implicitly by a relation between z and y such as r² + y? = 4. In such cases, differentiating with respect to a both sides helps us compute y = d. We should be careful, however, with the Chain Rule that needs to be applied in the way. That is, if y is assumed to be a function of æ, then (y²Y = 2y(3/) (e")' = (e");/ and so on. This process is called implicit differentiation. a) Apply implicit differentiation to find an expression for y = , in terms of x and y, in the following case: VE+ Vũ = 5 4. b) Now, start with the exact same equation as before, i.e. VI+ Vj = 5, but this time both r- and y– variables are assumed to depend on yet another variable t (the way it usually happens in Applied Calculus). This means that we will have to take derivatives with respect to t on both sides of the given equation and that we will encounter not only dy dt but also dr dt If dr = 5, dt find lip when r=4 and y= 9. dt 5. What is the most general antiderivative of the function f(z) = x° – 2, in other words, what is
Transcribed Image Text:4. Now, as explained in class, recall that some functions are defined implicitly by a relation between z and y such as r² + y? = 4. In such cases, differentiating with respect to a both sides helps us compute y = d. We should be careful, however, with the Chain Rule that needs to be applied in the way. That is, if y is assumed to be a function of æ, then (y²Y = 2y(3/) (e")' = (e");/ and so on. This process is called implicit differentiation. a) Apply implicit differentiation to find an expression for y = , in terms of x and y, in the following case: VE+ Vũ = 5 4. b) Now, start with the exact same equation as before, i.e. VI+ Vj = 5, but this time both r- and y– variables are assumed to depend on yet another variable t (the way it usually happens in Applied Calculus). This means that we will have to take derivatives with respect to t on both sides of the given equation and that we will encounter not only dy dt but also dr dt If dr = 5, dt find lip when r=4 and y= 9. dt 5. What is the most general antiderivative of the function f(z) = x° – 2, in other words, what is
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