(a) Find dy if y= 1+2x² dx

Q: Solve for dy/dx and dx/dy: 8xy+2x^4y^-3=x^3

A:

Q: (3y + 2x) dx –x² dy = 0, given that x = 1, when y = 2

A:

Q: 5. Find dy/dx (y - x)? = 2x + 4

A: Given: y-x2=2x+4 To find dydx. Solution: Power rule of differentiation states that: ddxxn=nxn-1…

Q: Find dy dx If y = 1- t² and x = 4+²

A:

Q: dy - xy3 -2xy %3D dx

A:

Q: Example 19: (a) Ifx +y = 25, find dy/dx.

A: Given function is x2+y2=25  …(1) We have to calculate dydx. The power rule of differentiation states…

Q: ∫ 2y dx + 3x dy   where d is described by 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

A: Consider the given integral is, ∫2ydx+3xdy The above equation is of the form M=2y and N=3x. Then, by…

Q: Find dy/dx given xy2 + x²y5 – x³ = 3 %3D -

A: Given that : xy2 + x2 y5 - x3  = 3. Find dy/dx . We know that d(xn)/dx = nxn-1.   Here i attached…

Q: dy + 4 y = x³ - dx

A:

Q: dy is dy xy dx dx The general solution of y² + x² "

A: Solution is given below:

Q: -3 dx dy 0, y2

A:

Q: Find dy/dx and d2y/dx2 without eliminating the parameter. x=1-t^(2), y=1+t

A: x=1-t2,  y=1+t Differentiating with respect to t, we get dxdt=0-2t  &  dydt=0+1⇒dxdt=-2t  &…

Q: Find dx/dy if y = x² + 1/x

A: To find dx/dy if y = x² + 1/x

Q: dy is : If x- y 0, then %3D dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find dy/dx if y = e-(1/10)e-x/2.

A: Given: y=e-110e-x2. To find dydx. Solution: Chain rule of differentiation states that:…

Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: bx a a dy dx 0. 0,

A: The value of the given double integration is ab/2

Q: 9. 3y'e" dx dy

A: To solve the integral

Q: Find dy/dx, if y=(x^2−2)^3 (2x+3)^4 dy/dx = _____

A:

Q: dy — х) %3D У(у + x) 2 - х(у dx

A:

Q: Find dy/dx if y2 = x.

A:

Q: dy dzy If y = e2x –2e¬3x, Find at x = 1 dx 'dx2'

A:

Q: y2 - cos(x²) + + 3x³ = 4x-3 dy 8. x – %3D dx

A:

Q: Find dy/dx if y2 =x.

A: Reframe the equation to obtain the equation for y. y=±x

Q: if y =(5x+1) 2x^-1 + INx then dy/dx will be

A: our objective is to find the derivative.

Q: dy e2x -3 Find if y = In %3D dx 1-4x

A: SOLUTION-

Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

Q: dy - 5y %3D dx

A: A differential equation is an equation in x,y and derivatives of y. A first-order differential is…

Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: dy - Sy = -xy* xy² dx

A:

Q: 16 dx -5y -0 dy dy 3

A: We solve this by ordinary differential equation

Q: Suppose that y = 2(x² – 2æ)-5. dy Find dx dy dx II

A: For the solution follow the next step.

Q: x In y dy dx -1J

A:

Q: Find dy/dx and dx/dy from 6x-x'y +4x 0

A:

Q: 19. Find dy/dx. y = x²

A:

Q: Find dy If y=1-t and x2 dx

A:

Q: *-Zy dy dx 2x

A: We need to integrate ∫02∫2x4e-x-2ydydx

Q: Find dy/dx, given that xy^3 -3y^2 +xy=1-3x

A: The main objective to calculate the derivative of the function xy3-3y2+xy=1-3x.

Q: dy い+ with dx y(-2) = 2 ニ - y x

A:

Q: if y =(ln x +1)(2x3 -3x), then dy/dx will be _________

A: Use the formula of differentiation of product of two functions to solve this problem.

Q: | Find dy/dx if y = e*+x).

A: Given,          y=ex+x2

Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

A:

Q: If y = (x² - 3x +2)(x² - 2), find dy/dx and evaluate dy/dx when x = -1

A:

Q: 17. dy dx = y2/3

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: 9) (x- y°-Ay-1) dx t 2x (x4 y +2)dy =o

A: As we know that the differential equation Mdx+Ndy=0 is exact, If ∂M∂y=∂N∂x. The solution is:…

Q: Find dx/dy  if y = 2x2+3/3x-1

A: Given that y = 2x2+3/3x-1 To find Find dx/dy

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.