Derivatives of Composite Functions

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Homework Help Overview

The discussion revolves around finding the derivative of a composite function, specifically y = f(x² + 3x - 5), at a certain point. The problem involves applying the chain rule and utilizing given derivative information.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of the chain rule, with one suggesting the use of g(x) to simplify the expression. Questions arise regarding the next steps after deriving the expression for dy/dx and how to apply the given information about f'(-1).

Discussion Status

Participants are actively engaging with the problem, with some providing suggestions for clarification and direction. There is recognition of the need to evaluate the derivative at a specific point, and the relevance of the provided derivative value is noted.

Contextual Notes

There is an emphasis on correctly interpreting the problem's requirements, particularly the need to evaluate at x = 1. Some participants express uncertainty about the implications of the given derivative information.

Dough
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I just need a nudge in the rigth direction ais don't know where to start
Let y = f(x^2 + 3x - 5) find dy/dx when x = 1, given that f'(-1) = 2

Thanks!
 
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Let g(x) = x² + 3x - 5, then y = f(g(x)). dy/dx = f'(g(x))g'(x)
 
i am not sure what else y have to do to get the answer, i wrote that out as well as

-1 = x^2 + 3x -5
solved and got x = 1 or -3...

but what else?

dy/dx = f'(x^2 + 3x - 5)(2x + 3)
 
Dough said:
i am not sure what else y have to do to get the answer, i wrote that out as well as
-1 = x^2 + 3x -5
solved and got x = 1 or -3...
but what else?
dy/dx = f'(x^2 + 3x - 5)(2x + 3)

I suggest going back and reading the problem again! You were asked to find y'(1). How about setting x= 1?
 
Very good suggestion.

And just to ease your worries, you were given a good piece of information: that f'(-1)=2. Do you see where this applies to the problem?
 

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