how that f(z) is differentiable and Evaluate f'(z) if f(2) = u(x,y) + iv(x, y), where %3D u(x, y) = cosh x cos y and v(x, y) = sinh x sin cos %3D

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

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Q: X- y – sin for its homogeneity. If it is homogeneous, give its degree. Test the function defined by…

A: For the solution of the problem follow the next step.

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Q: r cos(y) + y(e² - 1) x + 0 f (x, y) = ry x = 0.

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Q: The directional derivative of the function f (x, y, z) = x²z + xyz + y² in the direction of u = 2i +…

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Q: Find the gradient of f (x,y,z) = e^(x+y) cos(z) + (y+1)tan^(-1) (x) at the pint (0,0, pi/6)…

A: The function is given by fx, y, z = ex+ycosz+y+1tan-1x The point is x, y, z = 0, 0, π6 To evaluate:…

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

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Q: ch of the following is the result of differentiating both sides of the ation x sin(y)=In(x)+y² with…

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

Q: = cos(xyz) + ln x5 - sinh y² + 3z at P(-1, 3, 0) Given: f(x, y, z) af(x, y, z) Find: дz 0 1 3 0 None…

A: See the details solution in below

Q: Find the linearization L(x, y) of the function f(x, y) at the point. Then find an upper bound…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = tanh (x + 2y + 3z)

A: We have given fx,y,z=tanhx+2y+3z and we have to calculate fx,fy and fz

Q: The gradient of f(x, y) = e³ ª sin(4 · y) at (x, y) = (3, – 2) is defined as followed: V f(x, y) =…

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Q: cosz f(z) = 0< kl z - sinz f(2) = 0 < /z| f(2) = e=V², 0 < Izl 1- e ,0< /zl f(2) = f(2) = z - 1' 0 <…

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Q: The partial derivative of function respect to y* f(x, y) = x² + y/y? %3D

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

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Q: Using the method of Variation of Parameters, the particular solution y, for the NHLDE y"+y=sec x is…

A: We  have to find particular solutions

Q: The directional derivative of the fiunction f (x, y, z) = x²z+ xyz + y² in the direction of u = 2i +…

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Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

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Q: Being fa function with continuous first derivatives, defined by: z = ryf (x² + y°, cos(ry)) If we…

A: Solution:-

Q: Differentiate f(x) = ln(tanh^2 (x^3  + 2x + 1))

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Differentiate the function. F(t) = (ln(t))2 cos(t)

A: Product rule of differentiation:       Chain rule of differentiation:       some general…

Q: The gradient of f(x, y) = e³ ² sin(3 - y) at (x, y) = ( - 1, – 3) is defined as followed: V f(а, у)…

A: It is gradient vector by using partial derivative

Q: 3) Caputo derivative of order yof a [y] differentiable u function with y> 0 is given t 1 çDYu(t) =…

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Q: 3. у %3D С1 соs 2x + сz sin 2х 4. y = c1e2* + c2xe2*

A: We will solve the problem

Q: Test the given function for its homogeneity. If it is homogenous, give its degree. f (x, y) = x + y+…

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Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = 3 e* cos (yz), Po(0,0,0),…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = - 3 ex cos (yz),…

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

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Q: xy cos.x f(x, y) =+3y²

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Q: 7. By differentiation (and having a suitable choice of integrating constants) show that L. f(s) ds+…

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Q: The directional derivative of 2e" cos y at f(x, y) = -2e* cos y at (0, 7) in the direction of v =…

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Q: |(y) + (0,0) (x. y) (0,0) Show that the function f (x, y). is continuous at the origin however =…

A: consider the equation  f(x,y)=∑xyx2-y2x2+y2 ,0  x,y  #(0,0)xyx2+y2 where f(0,0)

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

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Q: i. y = x-% % -4Vx ii. y = x+Inx+ sin(3x) iii. y = x° cOS X y = x° cos x

A: Use product rule of differentiation

Q: f(x, y, z) = 6x y 25 V f(x, y, z) = %3D 5 f(x, y) = cos (6x) + sin (3y) = COS Vf(x, y) = %3D

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Q: sin(x² + y?) x2 + y2 (x, y) # (0, 0) Let f(x, y) = %3D 1, (x, y) = (0, 0). Show that f is continuous…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

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Q: Find the absolute extrema of the function on the closed interval. y = 5 cos x, [0, 2n] minimum (x,…

A: Solve the following

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

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Q: maximum rate of change of f(x, y, z) = tan(7x + 5y + 2z) at the point (2, – 2, 6).

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Q: 3) The directional derivative of the function g(x, y,z) = 3e* cos(yz) at po (0,0,0), in the…

A: "As per our guidelines we are allowed to solve only first complete question, repost other…

Q: 2″ Given f(x) = xr-¹e-λx, x > 0, r, λ > 0. Γ(r) 2. Evaluate etx f(x) dx. HINT: Express f etx f(x) dx…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.