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

Q: e sinh 2x dx

A: The given integral,       ∫e-xsinh(2x) dx

Q: e* + sin x = 2/xy , find y' %3D

A:

Q: dy Find of y=: dx InIn2r

A: We need to find derivative of y.

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: 1. S(1+ tanx)?dx

A:

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

A:

Q: " f e/2i =sin2 then z = = sin2 then z =

A: In the given question we have o find the value of z which satisfies the condition s.t e-z2i=sin2.…

Q: 7. Let y = tan (3x - 2), find y'.

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: If y = tan () , find y'

A:

Q: Find dy/dx: a. 3x? – (xy²)/2 = 2y³ b. y = (cosx – nx)^**

A:

Q: Compute for dy/dx. Suppose y is a function of x. a.) y = 2^(cotx) Arcsec(πx) + cos² (π/7)

A: Given: y=2cotxsec-1πx+cos2π/7

Q: Find dy /dx fors catx y-(tanx) +Ccata) (cotA) tanx

A: We use Logarithmic properties and differentiation

Q: Find y’ if y = Arc cos (sin 4x).

A:

Q: for y= 1hfe

A: Here, the given function is: y=ln(e-4x)  =(-4x)ln e  =-4x(1)  =-4x

Q: y = π/2 sinx y' =

A:

Q: Find y". y = 5 cot X

A:

Q: 1. /2х— х2 dx

A: Given ∫2x-x2 dx The given term can be rewritten as ∫2x-x2 dx= ∫2x-x2-12+12 dx so we get…

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: Find dy/dx

A:

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.