Partial and Total Derivatives

• 
  Differentiation of y with respect to t keeping x constant

• Differentiation of y with respect to both x and t

• Differentiation of y with respect to x keeping t constant

• None of these

The total derivative of a function f(x, t) with respect to t is:

• −Aωcos⁡(kx−ωt)

• −ωsin⁡(kx−ωt)

• −Aωsin⁡(kx−ωt)

• Aωsin⁡(kx−ωt)

• 4t³

• 2t

• 4t³+2t

• 4t

• −Akcos⁡(kx−ωt)

• −Awsin⁡(kx−ωt)

• Aksin⁡(kx−ωt)

• −Aksin⁡(kx−ωt)

• x

• 1

• t

• 0

• 2t

• t²

• x

• xe^xt

• e^t

• te^xt

• e^xt

• xcos(xt)

• cos(xt)

• sinx

• cost

In signal analysis, partial derivatives are used when:

• The signal is periodic

• The signal depends on both time and space variables

• The signal depends only on time
  

• The signal is constant