Let T= f(x,y) be the temperature at the point (x, y) on the circle and suppose that on the circle x = cos t and y = sin t, 0

Q: y=8sin(x)cos(x) ; x=pi/3

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Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: find the derivative of y with respect to x, t, orθ, as appropriate.

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Q: Find the derivative of y with respect to the independent variable. y = 9cos zO O A. - 19cos AO In 9…

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

A: Given:        x2+2xy=y3

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: Show that the function ex(cos y +i sin y ) is holomorphic and find its derivative

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Q: az Find dz by implicit differentiation, and confirm that the and dy results obtained agree with…

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Q: Is there a smooth (continuously differentiable) curve y f(x) whose length over the interval 0sxsa is…

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Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

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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 derivative of y with respect to x, t, or u,as appropriate.17. y = ln (u + 1) - eu…

A: Given, y=ln(u+1)-euDifferentiating both sides w.r.t u we…

Q: find the derivative of y with respect to x, t, or u,as appropriate.13. y = ln (t/2) 14. y = ln…

A: Given question is to find the derivative of the function , which can be solved by using the chain…

Q: Determine the points in the interval (0, 2T) at which the graph of the function below has a…

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Q: Find the derivative of y with respect to the appropriate variable 65. y = sV1 – s² + cos¯s 66. y =…

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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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: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y) =xy, What is…

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Q: Find the derivative w = sin* y cos*y a. sin³ 2y cos 2y b. sin² 2y cos 2y c.sin 2y cos 2y d. sin 2y…

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Q: Find the derivative, dy/dx: In-2x O y = -() In' 1-4 la > 是 In' x 2/1+2In ४ In' z In z 2w In² z ) In'…

A: This question is based on diffrentiation.

Q: Suppose that y is a differentiable function of x andz = cos (x4y9).Express  dz dx  in terms…

A: Given a differentiable function

Q: Suppose you want to use implicit differentiation to find dy and that: dr sin(a + y) = cos(xy) Which…

A: This question is related to implicit differentiation, we will solve it using given information.

Q: 2. Determine the directional derivative for u = log, x2lnz if it is defined by the direction at dx =…

A: Given u=logyx2lnzby the direction at dx=dz, dydx=2and is situated at a point in the Euclidean space…

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: Suppose that y is a differentiable function of x and w = sin(y2). Express the derivative of w with…

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

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

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

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Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Assume that x and y are both differentiable functions of t and are related by the equation y =…

A: Given :y=cos4xdxdt=-3 when x=π8 Use chain rule to evaluate the dydt. According to chain rule,…

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

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Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

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

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: Find the derivative with respect to x. (c) y = v7x – x4 (d) y = (1+ sin 7.x)-5 (a) y = (5x – 2)*…

A: This question is related to derivative, we will solve it using given information.

Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: Find the derivative of the following functions: = Arccos 4x -4 ans. y' = V1-16x2 4. y = Arcsec(sec…

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Q: Q6:- Show that R = (sin t)i + (cos t)j + v3k has a constant length. And R(t) is orthogonal to its…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that y is a differentiable function of x and w = cos(y5). Express the derivative of w with…

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Q: Let y be defined implicitly by the following equation as a function of x and z : eyz +sin(tyz) – xyz…

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Q: Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+y) =xy. What is…

A: We have to find derivative

Q: Find the derivative of y = Arccot (tan(esecx)) in its simplest form %3D A. y' = e Sec*secxtanx B. y'…

A: This question is related to differentiation, we will solve it using given information.

Q: 21: dz 22: Find the derivative of f(y,x) = xe?y + cos(3yx) at a point (1,0,7)in the direction of V =…

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Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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

A: Consider the equation 5xy-5x3=15 Here, the objective is to find dydt in terms of x,y, and dxdt

Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: The Derivative az/ax of sin(xy+z)-sin(zx- * :y)+sin(yz+x)=1 is -ycos(xy+z)-zcos(zx-y)-cos(yz+x)…

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. sin t (In t+5) 3 y e 3esint cos…

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: