2/6 Consider the upper half of the ellipsoid f(x.y) = 1--n and the point P-- 3 on the level curve f(xy) = Compute the slope of the line tangent to the level curve at P, and verify that the tangent line is orthogonal to the gradient at that point. Find the derivative of f(x.y) = dy dx

Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: Find partial derivative af dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2). Suppose that you…

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Q: Find partial derivative of dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

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Q: Show that the given femction satisties G-R Q. 4. conditions at origin but doesnot have a derivative…

A: Given we have given a function  f(z) = (x3-y3)+i(x3+y3)x2+y2,    if z≠0              0            ,…

Q: 3) (a) Find the oirectional derivative of f(x, y) = xe-y x at (-2,1) in the direction u= i-j. O…

A: We need to find the directional derivative in the direction of vector u

Q: The gradient of the tangent to the curve y=flx) at the point P(2, (2)) is given by A 12) – h f(2+k)…

A: To find the gradient of the tangent to the curve y=fx at the point P2, f2.

Q: 3. find the derivative of the function at Po in the direction of u. f (x, y,z) = 3e* cos yz,…

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Q: Obtain the gradient to a curve with parametnic equations given by and y= X= In 2 2t when t-1

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Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the…

A: The given function is f(x,y)=sin (xy) and the point is (4,0)=(a, b). to find : Maximum rate of…

Q: Find the derivative of y with respect to t. 3. 0<t< 2 y = sec 2t3 dy dt

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Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*…

A: We can answer all three subparts as below.

Q: Calculate derivative of the function y= 5t - 1e^t at t= 4 dy/dt |. = t=4

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Q: Find the maximum rate of change of f(x,y) =x²y+ /y at the point (1,1). In what direction does it…

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Q: Find the derivative of y with respect to t. 1 y3D cot dy dt %3D

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Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: Find the maximum rate of change of f (x, y) = xy ^ 2 + root (y) at the point (2,1). in which…

A: The maximum rate of change of f(x, y) happens along the direction grad(f) at the given point (2, 1).…

Q: 2. Find the equation of the tangent plane to f(x,y) = sin(x² +y) when x = 0, y = T. 3 and r - cost

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Q: Find the derivative dydx of the parametrically defined function x=t+2sinπt, y=3t−cosπt at t=12

A: Given X=t+ 2 sinπt        and   y = 3t- cosπt We have to find dy/dx at t=12 Method used  Chain…

Q: What is the equation of the curve whose tangent line passes through the point sec (In x) dx? (1,2)…

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Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs…

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: Given y(x) = cos(2x² – 2x), calculate the value of x when y is a maximum and when y is a minimum…

A: Given y(x) = cos(2x2-2x)  first we find the critical points using equation y'(x) = 0 . At critical…

Q: (3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by…

A: We will check whether the given function is total derivative or not. We also integrate dz pathwise.

Q: Consider the function g defined by 1 g(x, y) = cos (Tx /y) + log3 (r y) In what direction does g…

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Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: Find the derivative of the function f(x, y) = e³ at the point (0, 2) in the direction in which the…

A: The derivative of function f(x,y) can be determined by the gradient of the function,…

Q: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: H.W: Use the chain rule to find the derivative of w= x + y with %3D dw respect to t dt with x =…

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Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

Q: 3/20 What is the equation of the tangent line to the function y = e*- arcsin) at x= 0 ? A) y- -(1+)=…

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Q: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

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Q: 2. Given that arcsec 2) + (x² – y²)² = 2. (a) Find dy using implicit differentiation. dx dy usino…

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Q: Find the gradient of pthe function and the maximum value of the directional derivative at the point…

A: To finds the gradient of the funxction and the maximum value of thedirectioonal derivative at the…

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: H.W: Use the chain rule to find the derivative of w=x² + y² with dw with x cost+ sin t, y= cost-sint…

A: If w is a function of x and y and x,y are functions of t then we get by Chain rule, dw/dt=…

Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

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Q: iven y = at / bt²+ct 31 find dy/dt where a, b, and c are constants. Find the slope of the tangent…

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Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

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Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 2y + 3z) at the point (−9, 6, 2) and the…

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Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

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Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

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Q: V30 Consider the upper half of the ellipsoid f(x.y) = and the point on the level curve f(x.y) =…

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Q: (2) Find an equation for the tangent plane to the graph of z = where z = f(x, y) is implicitly…

A: Given: The function is fx,y,z=xy+xz+yz-lnz2+1-4. Calculation: Obtain thethe value of  fxx,y, fyx,y…

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

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Q: dy Find by using partial differentiation where y is defined dx implicitly as y=f(x) for the…

A: We use the chain rule and product rule to find the derivative.…