Use the total differential to find the slopes of the indiffa of the following utility functions: a) w(x, x2)= xX2, b) ú(x, x2) = xx3

Q: Find the equation of the tangent line and equation of the normal line to the graph of 3x cos y = 1 +…

A: We have to find the equation of normal and tangent line.

Q: Calculate the total differential dz for z = r sinh(ry) + yelv

A: Note- since you have asked multiple questions, So Acc. to Bartleby guidelines we are supposed to do…

Q: Find the total differential dz for z=tanh(y)ln(x)

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Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: Use the chain rule to find the derivative of w= x + y with dw with x cost + sint, y= cost– sint dt…

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Q: Find the total differential, given: (b) \theta = arctan (y/x)

A: Let us consider the function z=f(x,y)  The partials derivative are obtained as…

Q: Find the value of the derivative of ƒ(x, y, z) = xy + yz + xz with respect to t on the curve x = cos…

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Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx %3D b. du = * c. du =-…

A: dx9-4x2=dx32-2x2 Put, u=2x⇒dudx=21⇒du=2 dx

Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: Find the partial derivative of the function with respect to each variable. h(p.p.0) = p sin o cos 0…

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Q: Find the tangent line to the curve x cos y + y cos x = 1 at (0,1). O A. (cos 1)æ + y = 1 O B. x + y…

A: We can find the tangent line as below

Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: x2y2=2y3+1

Q: Find the total differential. z = x cos(y) – y cos(x) dz =

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Q: This is a linear DE. If arranged to its form, what is the integrating factor? * xdy ニ

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Q: Find the derivative of the following indefinite integral or partial area function: I(x) - sin t? dt

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Q: Use a linear approximation (or differentials) to estimate the given number to the nearest hundredth.…

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Q: Find the differential of the function y=arcsinuv, where u and v are differentiable functions of x.

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Q: Let y = f(x), where f(x) = 6x2 + 3. Find the differential of the function. dy =

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Q: . f(x, y) = y*e*Y at (0.2, 1.96)

A: Use differential formula to find approximate value.

Q: Find ðw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s +t, y…

A: We will find out the required value.

Q: Find the total differential of the following: 1. f(x, y,z) =-tan'(x + y +z)+ In(xyz)

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Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Find the derivative of the following integrals: (a) (**at) (b) (LA dt) Vt +1

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Q: 3. ) Compute for the increment of the function f(x,y) = *+3y . Also, find the total differential of…

A: w = f (x, y) and let ∆x and ∆y be increments of x and y respectively. The increment ∆w of w = f (x,…

Q: Write the approximate change formula for a function z = ƒ(x, y) at the point (x, y) in terms of…

A: Consider the following function: z=fx,y

Q: Find the total differential. z = 10x6y7 dz = %3D

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Q: Find the total differential of z= f(x, y), where f(x, y) = In Use * for multiplication of variables,…

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Q: Suppose that x and y are both differentiable functions of t and are related by the given equation.…

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: Differential

Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: Find dw/ds and dw/dt using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x-s+t, y =…

A: The given function,w=sin(4x+5y)x=s+ty=s-tat the point s=0, t=π2

Q: Find the differential of each function. (a) y = etan(nt) tan(at) · soc2 (at) - T dy = sec“(at) · T e…

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Q: Let L be the length of the curve y = ln x from (1, 0) to (e,1). (a) Integrating with respect to x,…

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Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

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Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k. %3D dr dt

A: Given

Q: 2) Find the total differential dz for z = tanhy In(x)

A: Total differential of z is given by dz=(∂z/∂x)dx+(∂z/∂y)dy

Q: Find ôw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(7x + 8y) x = s + t, y…

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Q: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: Find the total differential. z = x cos(y) -y cos(x) dz %3D

A: A scalar function f(x,y) is a rule that is used to associate a number or quantity with a particular…

Q: Find the total differential. z = x sin xy

A: Given: z=x sinxy To determine: The total differential of the given function.

Q: Find the total differential. z = e4x sin(3y) dz =

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Q: Find the total differential of the following: 1. f(x, y) = sin x+ ye 2. f(x, y, 2) = – tan"(x+ y+ z)…

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Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: Find an (1,1) equation of the tangent i ine at the curue yt+xy = x_x+a. on

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Q: 4. Find the total differential of z = In(x + y), x= w, y = w². By how much will z change if w…

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Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

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Q: Show that r = (sin t)i + (cos t)j + V3k has a constant length. And r(t) is orthogonal to it's…

A: Note: We are supposed to answer only one question. Kindly repost other questions as to the next…