a) Find dz, if z = e' sin e %3D b) Verify uxy = uyx , if u = In /x² + y² . %3D

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: 3 1 13. Jisc(2)csc (2x)cot (2x)dx cresc 8 Type. U = U' =

A:

Q: Find the dy/dx for y=cos^2(3πt-4)

A: y=cos2(3πt−4)y=(cos(3πt−4))2u=cos(3πt−4)y=u2 dudy​=2u(Power Rule:…

Q: y = π/2 sinx y' =

A:

Q: Find y". y = 5 cot X

A:

Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: If u=e*? then du= ... %3D dx 2xe* dx 2x 2xe*

A: The chain rule states that ddxfgx=f'gxg'x.

Q: (b) 를/ dx 3

A:

Q: Evaluate 2 Cot 2 / dx ct x 3 k 742

A: The given integral

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.