Found the line of differentiability of f(z)=x2 - 2xy + 3y + i(2xy - y2 +x)

Q: ) Estimate the value of Csc (0. 2) using linear approximation and without using any kind of…

A: Given problem:- Estimate the value of csc(0.2) using linear approximation

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

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Q: Find the points on the curve y=x(x-1)(x-2) which have the same gradient use @ for 2

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Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Find an equation of the line tangent to f(x) =3 at x 3. %3D OA. y=xln 3+ (1– 3ln 3) OB. y=27(xln 3 +…

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Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

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Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

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Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

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Q: Find the derivative of the function. y = x 5 Vx3+7 O y'=- 2VX3+7 3x7 5x3 Vx3 +7 3x6 O y'=. 5x4 Vx3…

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Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

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

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Q: 3. Find the derivative of the function f(x, y, z) = xy³ + yz³ + zx³ at the point (-1, 2, 1) in the…

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: Find the maximum rate of change of f (x, y) = xln /x2 + y2 at (1,2) and direction in which it…

A: To find the maximum rate of change of fx,y=xlnx2+y2 at 1,2 and direction in which it occurs.  First,…

Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: What is the gradient of f=x^2+y^2-2xy-x+3y-z=-4 ?

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Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

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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: The directional derivative of f=8x°y-2xy2+3z at point P(1,1,2) in the direction 2âx+2ây-âz is

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Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: _6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 -…

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Q: Find the derivative of f(z) = 3+ 2x² – 2y² + i4xy .

A: We find out the derivative of given function .we differentiate both sides with respect to z and take…

Q: the derivative rules to find the dervative of y. Use y= (9-x²)% y = : 13-2x y= V9x2+ 2x+7 y=…

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Q: The derivative of f(x) = 9z3 12 8. is %3D 3z f'(x) O f(r) – 9x?+ 12x 4 – 9r– 12x + 8e 7 O f(r) - 9x…

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Q: 2. Find y' by implicit differentiation. (1) xy-3x+2x =8 (2) 9x² +4y² = 25 (3) x²+2xy- y² =5 2 3 = 6…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the derivative of f(z) = (x³ + 5)(z³ – 5) %3D (8z")(5x*) (8z +5)(z – 5) + (z³ + 5)(5x* – 5) (8z…

A: We need to use the product rule.

Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: The directional derivative of f=8x²y-2xy²+3z at point P(1,1,2) in the direction 2âg+2ây-âz is

A: First we find the gradient of the function f and then unit vector.

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Use the first derivatives test to find the local exterma of f(x) =x3-12x on R

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Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: 2. The derivative of y = (1 + Vx3) (x3 -2 V) is y'=-3x4-3xs-2z2-11xº.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor…

A: A. Profit Function : P(X) = R(x) - C(x) P(x) = -0.04x2 + 800x - 130x + 40000 P(x) = -0.04x2 + 670x +…

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: Find the linearization of the function z =/ at the point (-5, 1). L(1, y)

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Q: Find the derivative of the function f(z) = 3z² +7z at I = a.

A: Given,            f(x) =3x2 + 7x  and x=a

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

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Q: Find the derivative of f(z)=((11z+4)1/2)(e3z).

A: Given function f(z)=11z+412e3z

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: