Q2. Find of y = 4x/x + V at x = 1? dx

Q: 1 I = J dx (1-x²)Z %3D 3

A: It is known that: 1-cos2x=sin2x∫sec2x=tan x+Ctansin-1x=x1-x212

Q: 1. L= V1 + 16x6 dx

A: First, we factor out 16 from the radical term, So, it becomes,

Q: dx 35. ex/2 +1

A:

Q: S(3 – x) dx 12

A:

Q: Vx³ Inx dx In x dx 1

A:

Q: Find √√3 x² +3 x² +1 dx

A:

Q: dx XI. Vx(x+1)

A: Here I am attaching image so that you understand each and every step.

Q: Find dx2 7x y = - - 5x 4

A:

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: Differentiate the function. y = (3x- 1)* (4 - x5) 3 dy dx II

A: To differentiate the given function:

Q: r=secxcscsx dr/dx=

A:

Q: dy Find for y = x(4x + 3) dx - |3

A: The function is given by y = x4x+313 To evaluate : dydx

Q: 2. ſ xºcos(4x)dx

A: ∫x0 cos4xdx

Q: y=coth 1/x

A:

Q: Differentiate implicitly to find dx 2y? - xy + 3x = 4 dy dx

A:

Q: Find f''(x). f(x) = (x² + 1) ⁹

A: Here we have to find the double derivative of the given two functionsy=(x2+1)9and y=-7x6+1Here these…