F(x) = F' (2) , where (t4 - 3t2 )dt %3D d. Vt dt x2 dx

Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

A:

Q: xy = 4x + 5y2

A: We will differentiate with respect to  X .

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: Find dy / dx by implicit differentiation. xy + 5x + 5x2 = 2 dy / dx =

A: xy+5x+5x2=2

Q: [2 ln (x)+1] dy in yty cosy %3D dx

A:

Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

A:

Q: Find the derivative of y = = Ve-5t +1 dy dt ||

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Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: Determine the anti-derivative of Y = 2e3x +5 and use the fact that y(0) = 7 to %3D dx determine c,…

A: We first separate the variables and then integrate  c= integrating constant Formula used:

Q: Find the total differential. z = 10x"y3 dz =

A:

Q: The integration of dx is 4+x²

A: The given integral ∫dx4+x2 can be evaluated as, ∫dx4+x2=∫dxx2+22                =12tan-1x2+C…

Q: Find dy/dx by implicit differentiation. 8.r2y+ 5yr = -9 y 5y + 16x 2x 4x + 5y dy/dx = %3D

A: Recall: d(u.v)dx=udvdx+ dudxv d(xn)dx=n xn-1 d(c)dx=0 ; where 'c' is any constant.

Q: Find dy/dx by implicit differentiation. x3y3 − y = x

A: Consider the following equation: x3y3-y=x                    ...... 1

Q: find dy/dx by implicit differentiation xy + 2x + 3y = 1

A: Consider the following equation: xy+2x+3y=1 Differentiate the above equation with respect to x.…

Q: Find dy dx2 by implicit differentiation. x y + eY d2y %3D dx2

A: Note: As per company's guidelines, we should solve only one question. So, kindly post the next…

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: x* + x²y² + y³ = 5

A:

Q: 16. ху : Vx2 + y?

A: Using implicit differentiation.

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

A:

Q: Find dy/dx by implicit differentiation. 8x3 + 9y3 = 66 dy/dx =

A:

Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: Find dy/dx by implicit differentiation. 6,,3 x°y - y = x dy/dx

A: On implicit differentiation we differentiate both sides of the equation with respect to x . Then we…

Q: Find dy/dx by implicit differentiation. 2(x^2+y^2)^2 = 25(x^2-y^2)

A:

Q: Find dy/dx by implicit differentiation. 5x?y + 4y2x = -5 dy/dx =

A:

Q: find dy/dx by implicit differentiation ex+2y = 1

A: Given Function is ex+2y=1

Q: Find dy/dx by implicit differentiation. x3 − xy + y2 = 7

A: Given : x3 − xy + y2 = 7

Q: dy/dx of y=sec^-1 (5x)

A:

Q: Find dy/dx by implicit differentiation. 2. Vxy = 5 + x²y dy/dx

A: Let's find.

Q: Find dy/dx by implicit differentiation. x4y1/4 = 18x+6y6

A: This question is based on the differentiation of Implicit function.

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: The number of hours of skilled labor is y and unskilled labor is x.

Q: Find dy/dx by implicit differentiation. 5x3 + x2y − xy3 = 2

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: Find dy/dx by implicit differentiation. 4x° + 9y3 - 62 dy/dx =

A: We use Implicit differentiation

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

A:

Q: Find dy/dx by implicit differentiation. x3 + y3 + 13y – 10 = 0 dy/dx =

A:

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: dy Obtain general solution of- 3/xy dx

A:

Q: Find dy/dx by implicit differentiation. 8x3 + x?y - xy3 = 2 dy/dx =

A: Solution: 8x3+x2y-xy3=2

Q: Find dy/dx by implicit differentiation. 72 – 5y² = 4 dy/dx =|

A:

Q: Find dy/dx by implicit differentiation. 5x2 + y² = 25 dy/dx = %D

A:

Q: The integrating factor of the equation (2 + y + x) dx + xydy = 0 is

A:

Q: Find dy/dx by implicit differentiation. xy = 8x + 9y2   dy/dx= ?

A:

Q: Find dy/dx: solution in handwritten 1. y = 5* (** + dx VE х4 3 -x²,

A: Using leibnitz rule for integral.

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: Find dy/dx by implicit differentiation. y cos(x) = 4x2 + 5y2

A: To find dy/dx by implicit differentiation,  given y cos x = 4x2+5y2

Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

A:

Q: Find dy/dx by implicit differentiation. VTy = x'y +33 dy/dx =

A: The given equation is xy=x7y+33.

Q: Find dy/dx by implicit differentiation. 5x^(3)+x^(2)y-xy^(3)=-8 dy/dx=?

A: We are given an implicit equation as