(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Knowing: y(x,t) = Acos(kx-ωt)

Find the partial derivatives of:

1) dy/dt

2) dy/dx

3) d^2y/dt^2

4) d^2y/dx^2

2. Relevant equations

3. The attempt at a solution

These are the answers the actual answers:

1) dy/dt = ωAsin(kx-ωt) = v(x,t) of a particle

2) dy/dx = -kAsin(kx-ωt)

3) d^2y/dt^2 = -(ω^2)Acos(kx-ωt) = a(x,t) of a particle

4) d^2y/dx^2 = -(k^2)Acos(ks-wt)

now here are my questions:

1) how come when I do the partial derivative of y with respect to t, kx becomes the constant and vice versa with dy/dx, how come ωt becomes the constant? is it because of implicit differentiation?

2) What does it give me to find: dy/dx? the slope? also what about d^2y/dx^2?

Thanks for the Help!

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# Homework Help: Partial derivatives with Wave Function

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