: )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

Q: 1. Dx[arcsin(2x + 1)]

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Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

Q: 2 [(3 sec2 x + - x)dx 4

A: Integrate

Q: dy for the following functions : dx 1. Find 3(x – 1) (ans.: 5) Sec² /2x +7 15) y=\tan /2x +7 (ans.:…

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Q: Find dy/dx and simplify results: 4xy-2x^3+3/4

A: Given: y=4xy-2x3+34 To find dydt

Q: y = () Зx2-2 х+3

A: I am using the chain rule to find the first order derivative of the given equation

Q: dy Use implicit differentiation to find dx 2х - 3 5y? 2x +3 dy dx

A:

Q: 1 √₁-² 1- Evaluate -dx (1 - 3x)²

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 2 dr x>1 rVF - 1

A: We will find the integral as following.

Q: 8. f sec² (3x - 1) dx

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Q: sec? (1/x) dx. 9: (16pts) Evaluate

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Q: fostp Ex=(Xzy)=-3:52-25)

A:

Q: y-Castesinz şinz

A: The detailed solution is as follows below:

Q: Y"+y=secxtanx

A: Given, y'' + y = secx tanx This is a second order linear, non-homogeneous ODE. We can write the…

Q: Ssec? [sec(4x)tan(4x) dx (p sec (5x +3) dx e) f sin 3x + 1. dx 2x +4 f)

A: We will solve the following

Q: Differentiate y = (ln r)tan 2x

A: We have to differentiate; y=lnxtan(2x)  taking natural logarithm both of sides;…

Q: * Salne the equalion:- (2x-44 +5)y'=n -2y+3

A: This homogeneous differential equation is solve by substitution and then by separation of variables…

Q: Differentiate, hcx) = In (x-Vr

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Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

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Q: Sel+x3/2 Vx dx ,1+3 X,

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Q: Find the derivative, A. C. 3x 6x² +2 (1-3x2)2 dx' of y = B. D. 2x 1-3x² 12x (1 - 3x²)² 2x 3(1-3x²)²

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.