Approaching Jacobian Calculation for a Single Function with Multiple Variables

[ver_mathstats]

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)?

 

[fresh_42]

Yes. The Jacobi matrix is simply the gradient in this case.

 

[ver_mathstats]

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)."