Find the linearization of y=e^squareroot 7x. at x=36.  (Use symbolic notation and fractions when needed) L(x)=

Q: 6. Parallel to the line Y = = -}(x – 100) – 99, 3 4 passing through (1, 3)

A: Given query is to find the equation of the line passing through (1,3) and parallel to the line…

Q: A point is moving on the graph of y³ = x². When the point is at (-512, 64), its y coordinate is…

A: Given, A point is moving on the graph of  y3 = x2. When the point is at -512, 64, its y coordinate…

Q: exy -2x+24

A: Consider the equation

Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Find the derivative. y= In x+3 %3D

A:

Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

A:

Q: Use a linear approximation to estimate V65.

A: 653

Q: Find  y''  by implicit differentiation. 4x2 + y2 = 4

A: Given,  4x2+y2=y,we have to find y''Differentiate with respect to x,we get…

Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

A:

Q: Use the limit definition of the partial derivative to verify the formulas

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

A:

Q: Suppose that the demand for a product is given by q2p=6,000, where q represents the number of units…

A:

Q: Find the derivative of the function. y = 3x + V3 3x + V3x y' =

A:

Q: Find the equation for the y perpendicular trajectories of the curve family. 1. x

A: perpendicular trajectory

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

A:

Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

A:

Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Compute the derivative of ln r3 –1 V2x+5x²

A:

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: Find the orthogonal trajectories ofthe family of curves: y = ke*

A: As per our company guidelines we are supposed to answer only first question. Kindly repost rest of…

Q: Еxample 5 1 1- Vxdx ха 0,

A:

Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: 9. y = 3x – Vx

A:

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

A:

Q: Estimate 3√9 using a linear approximation at a=8.

A:

Q: Find the first and second order derivative w=3z7-7z3+21z2

A:

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: If 3x + 3x + xy 4 and y(4) = - 14, find y' (4) by implicit differentiation.

A: According to question,Given equation,3x2 + 3x + xy = 4,y4 = -14

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.8x2 −…

A:

Q: 7. y = Vx + 2

A: Using Delta method differentiate y. And using rationalising.  Follow step 2nd  .

Q: If 5x^2+2x+xy=4 and y(4)= -21, find y’(4) by implicit differentiation.

A:

Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

A:

Q: Find the second derivative of y = -5 %3D -

A:

Q: the Chain Rule.

A: Given: y=11-x46. Let, u=1-x4 By chain rule, the derivative of y with respect to x is given as,…

Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Find y'' by implicit differentiation 4x3+3y3=6

A:

Q: Find y" by implicit differentiation. 4x3 + 5y3 = 1 y" =

A: We will find the y" of the given function using the implicit differentiation.Below find the solution…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: * Use the chain rule to find the derivative of

A: Given,        w = xy Here,         x=tan(t),   y=csc(t)

Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

Q: Calculate the second and the third derivative of y = 5x- 9 y": y"

A: Using derivatives rule & formula.

Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

A: