Evaluate this function of z = cos x sin y; x = u – v, y= u² + v². Use chain - dz rule to find ди А. 2ucos (u – v) cos (u? + v²) – sin(u – v) sin(u² + v² ) - В. 2usin (u – v) cos (u² + v²) – cos(u – v) sin(u² + v²) COS - - С. 3ucos (u – v) cos (u? + v²) + sin(u – v) sin(u² + v² ) | D. 3usin (u – v) sin(u? + v²) + cos(u – v) sin(u² + v² ) -

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Q: PDE ut- 3leuxx 0LXLI も>6 B.C.: : ulo,t) = ULyt)=D0

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Q: Find (u+v).(2u-v) given that u.u=4, u.v=-5 and v.v=10 Determine if u and v are orthogonal…

A: Given, u·u=4, u·v=-5, v·v=10

Q: дz az Use the chain rule to find and Əs Ət əz Əs əz at = = ¹(=), z = tan u = 3s + 5t, v = 5s - 3t

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Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

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Q: Write the function f(z) = z + 1/z in the form f(z) = u(r, theta) + iv(r, theta) (Answer is f(z) = (r…

A: f(z)=(r+r1​)cosθ+i(r−r1​)sinθ   Explanation:

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Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

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A: The given function,        zsin3xz+y2

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Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

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