Approaching Jacobian Calculation for a Single Function with Multiple Variables

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To calculate the Jacobian for a single function with three variables, the function can be expressed as (s^2 + sin(rt) - 3)/s. The Jacobian matrix is represented as J = [∂f/∂s ∂f/∂r ∂f/∂t], with the specific values substituted as (1, π, -1). In this scenario, the Jacobian matrix effectively acts as the gradient of the function. The discussion confirms that the approach is correct and clarifies the function's formulation. Understanding this method simplifies the calculation of Jacobians for single functions with multiple variables.
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Homework Statement
We must find the Jacobian of f(s,r,t)=s^2+sin(rt)-3. Compute J(f/s)(1, pi, -1).
Relevant Equations
f(s,r,t)=s^2+sin(rt)-3. Compute J(f/s)(1, pi, -1).
I'm used to calculating Jacobians with several functions, so my only question would be how do I approach solving this one with only one function but three variables?

I think our function becomes (s^2+sin(rt)-3)/since we are looking for J(f/s). So then would our Jacobian simply be J=[∂f/∂s ∂f/∂r ∂f/∂t] with finally our values substituted of (1, pi,-1)?
 
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Yes. The Jacobi matrix is simply the gradient in this case.
 
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fresh_42 said:
Yes. The Jacobi matrix is simply the gradient in this case.
Thank you, and sorry for the typo, I had meant "I think our function becomes (s^2+sin(rt)-3)/s since we are looking for J(f/s)."
 
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