Solve first order partial derivatives

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SUMMARY

The discussion focuses on solving first-order partial derivatives of the function g(s,t) = f(s, u(s,t), v(s,t)), where u(s,t) = st and v(s,t) = s + t. Participants emphasize the use of the Chain Rule to derive the partial derivatives with respect to s, u, and v. The key takeaway is that partial derivatives are calculated by holding all other variables constant during differentiation, which is crucial for understanding the problem's requirements.

PREREQUISITES
  • Understanding of Chain Rule in calculus
  • Familiarity with partial derivatives
  • Knowledge of functions of multiple variables
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the application of the Chain Rule in multivariable calculus
  • Practice calculating partial derivatives with various functions
  • Explore examples of functions defined in terms of other functions
  • Learn about higher-order partial derivatives and their applications
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Students studying multivariable calculus, educators teaching calculus concepts, and anyone seeking to improve their understanding of partial derivatives and the Chain Rule.

jimjames
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Homework Statement


Use the Chain Rule to find the 1. order partial derivatives of g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t) = st & v(s,t)=s+t
The answer should be expressed in terms of s & t only.

I find the partial derivatives difficult enough and now there is no numbers in the problem, which confused me even more. Hopefully someone here can help me with how to solve this.

Homework Equations


g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t) = st & v(s,t)=s+t

The Attempt at a Solution


(I have no idea what to do with this problem)
 
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jimjames said:
(I have no idea what to do with this problem)

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation.
so calculate the partial derivatives with respect to s, and u and v whwere the partial derivative with respect to s will be taken when u.v are lept constant and in turn for the other two.
 

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