Find the value of c such that satisfies the heat flow equation f(x,y,t) = ect.sin(4x) cos(6y) ft = fxx + fyy.

Q: Find dy/dx. x = t sin(t),    y = t2 + 6t

A: given ,        x = t sint        y = t2 + 6t

Q: If y = 2x3 + 5x and dx = 2, find dt dy Y when x = 4. dt dy - dt

A:

Q: Differentiate with respect to t. y = 7sin(x - t) -(7sin(x-t)) = dt

A:

Q: Use the Chain Rule to find dw/dt. dw dt = w = In x² + y² + z², x = 3 sint, y = 8 cost, z = 6 tan t

A: So, After the differentiation the final answer for the question is:…

Q: Find dy Sin (x-qy) xe %3D 24 dx

A:

Q: If V = x² + y² where, x = a cos t, y= b sin t, find AP and verify the result. dt

A: x=acost y=bsint V=x2+y2 put the values of x and y V=acost2+bsint2 V=a2cos2t+b2sin2t

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

Q: Express the function f(z) = sin(=) in the form f(z) = U (x, y) + V (x, y)i. %3D

A:

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: