How Do You Apply the Chain Rule to Differentiate h = 3x^2y^3 with Respect to t?

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Homework Help Overview

The discussion revolves around differentiating the function h = 3x^2y^3 with respect to t, utilizing the chain rule. Participants are exploring how to apply this rule given specific values for x and y, as well as their rates of change.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks guidance on how to start differentiating h with respect to t, given the values of x, y, and their derivatives. Some participants reference the chain rule and provide a formula for differentiation, while others express confusion and request simpler explanations.

Discussion Status

The discussion is active, with participants attempting to clarify the application of the chain rule. There is a mix of understanding and confusion, with some guidance offered but no clear consensus on the best approach yet.

Contextual Notes

Participants are working under the constraints of specific values for x and y, as well as their respective rates of change, which may influence their interpretations and approaches to the problem.

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h = 3x^2.y^3
find dh/dt, if x=1, and y=2
Also, dx/dt = 0.2, dy/dt = 0.1

Any ideas where i should start in order to get this out?
Thanx
 
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[tex]\frac{dh}{dt} = \sum_i \frac{dF}{dx_i}\frac{dx_i}{dt}[/tex], you have the expression for [tex]h[/tex] and the points at which to calculate the final answer.
 
I don't understand that expression, can you simplify your explanation please
 
If x is a function of t, f(x)= x^2, what does the chain rule say
df/dt is?
 

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