Solve first order partial derivatives

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To find the first order partial derivatives of g(s,t) = f(s, u(s,t), v(s,t)), where u(s,t) = st and v(s,t) = s + t, the Chain Rule is applied. The challenge lies in differentiating with respect to s and t while treating u and v as constants during each differentiation. The process involves calculating the partial derivatives of f with respect to its variables, followed by applying the derivatives of u and v with respect to s and t. This results in expressions for the partial derivatives in terms of s and t only. Understanding the Chain Rule is crucial for solving this problem effectively.
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.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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