Differentiation (Trig Function)

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Homework Help Overview

The discussion revolves around taking the second derivative of the function cos(x^2), focusing on the application of differentiation rules, particularly the product and chain rules in the context of trigonometric functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the initial derivative calculation and express uncertainty about proceeding to the second derivative. Questions arise regarding the appropriate rules to apply, particularly the product and chain rules, and how to combine them effectively.

Discussion Status

Some participants have provided guidance on the necessary rules to use, while others express confusion about applying these rules to composite functions. Multiple interpretations of the derivative process are being explored, and there is no explicit consensus on the final approach.

Contextual Notes

Participants indicate challenges with understanding the combination of differentiation rules and the handling of composite functions, which may be influenced by imposed homework constraints.

SciGuy26
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Homework Equations



Take the second derivative of:
cos(x^2)

The Attempt at a Solution



cos(x^2)

dy/du = -sin(u)
du/dx = 2x

dy/dx= -2xsin(x^2)

I don't know how to begin taking the derivative of this a second time...
 
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What rule do you think you will need to use?
 
Use the product rule with -2x and sin(x^2). You'll have to use the chain rule again when you calculate the derivative of sin(x^2).
 
So I'd have 2xcos(u) + -2sin(u)

How am I to use the chain rule at this point?

Ugh I don't understand how combine rules with composite functions.
 
nm...

Solution should be as follows:
-2xsin(x^2)

dy/du= sin(u)
du/dx= 2x

-2xsin(u) + -2xsin(U)

-2xcos(u) + -2sin(u)

= 2x(-2xcos(x^2) + -2sin(x^2))

Could someone please confirm? Thank you for the help.
 

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