Show that u = 3x^2y + 2x^2 - y^3- 2y^2 is a harmonic function.

Q: Find the slope of the line tangent to the graph of y= sin3x at x=pie/6

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Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Use implicit differentiation to find y' for 5æ y? + In(xy) = Preview 5.

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Q: An equation of the tangent line to the curve y= 4x2-8x-5 at the point (-1, 5) is O y14x-9 Oy 14x71 O…

A: The curve is given by,

Q: (2х-6)° $(x) = (2x-6)* (x+3)'

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Q: Find the second derivative of the funcion. y%3D

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Q: Choose the correct answer by using the Product rule of derivative. d dx - (x4.x7) is equal to…

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Q: The derivative of sec2 2x(cos2x−sin2x) with respect to x is

A: Given: f(x)=sec2 2x(cos2x−sin2x)   Simplify the function before finding the derivative: By  the…

Q: Locate the discontinuities of the function andillustrate by graphing.        y = 1/1 + sinx

A: given: y=1/1+sinx

Q: Xyz. %3D Use implicit differentiation to find az/ar

A: The given function is ez=xyz.

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: Verify the formulas by differentiation. ∫ sec2 (5x - 1) dx = 1/5 tan (5x - 1) + C

A: ∫sec25x-1 dx=15tan5x-1+C

Q: Compute the derivative of f() = arcsin(x² e3x). %3D

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

Q: what is the implicit differentiation of: ysin2x=xcos2y

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Q: 1. у %3D 4x? — Зх — 2.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: If tanx   =12/13 , find the values of the other hyperbolic functionsat  x.

A: tanhx=1213 By using the identity sech2x+tanh2x=1, we get…

Q: The slope of the tangent line to the parabola y 3x2 + 2x + 6 at the point (5, 91) is: The equation…

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Q: Find the slope of the line tangent to 2xy + π sin y = 2π through the point (1, π/2).

A: The slope of the line tangent to 2xy+πsin y=2π through the point 1,π2.

Q: theoretically define what is the derivative of a transform and what is its function

A: Given data is : Define what is derivative.

Q: Find the derivatives of the functions in Exercis

A: we have to find the derivative of the given function. g(t)=1+sin3t3-2t-1

Q: Find the derivatives of the functions in Exercis

A: Given, y=5-2x-3+182x+14

Q: Question 3

A: Consider implicit equation and

Q: Find anti derivative of 4cscxcotx + 3/(sqrt(1-x2) - 1/(cubrt(x5)

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Q: Find the derivative. 5х + 1 In 5x - 1 dx 5x +1 %3D dx 5x -1)

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Q: 2. у %3D 3 + 4x — х?

A: We can find the answer as below

Q: Ax) = (5x* - 3x)(2x° – 7x) en x =

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Q: Verify the differentiation formula.

A: Given Data The differentiation formula is .   The formula of sech x is, The left-hand side of the…

Q: omplex derivative of (Log z)^3

A: Given: log z3 To find: The complex derivative of given function.

Q: Find first and 2nd derivative guncic 2 tan2x 3.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Which hyperbolic functions are increasing on their domains?

A: First of all, consider all the six trigonometric hyperbolic functions and their domains.

Q: rconh(3x+1) - 5t +ldt f(x)= sinh³

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Q: 1. у %3D 4x2 — 3х — 2.

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Q: Find the equation of the tangent and the nirmal to the curve y=5x4 at the point (1,5)

A: Given curve,  y = 5x4  To find the equation of tangent and normal at the point (1, 5)

Q: Find all points on the curve 3x + 6y² = 36 where the tangent line also passes through the point (10,…

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Q: sec- 1 2. у %3D| tan

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Q: Find the first derivative by applying the appropriate rules. DO NOT SIMPLIFY the algebra. (a) fx)…

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Q: 1, cosX, cos 2X,--- , cos mx

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: Find the second derivative of y = -5 %3D -

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Q: 1. y= ArctanB %3D 3-V9-x2

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Q: 5z²)* 4/3 %3D

A: (3). The function is given by Hz = 1-5z243 To evaluate: The derivative of the function.

Q: Find the third derivative of y = (8x 1) solution and upload it on the designated field in jpeg or…

A: The given equation is y=8x-114to find the third derivative of the given function. Differentiation is…

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: Sketch a graph of y = 2x on [-1, 2] and use geometry to find theexact value of function given

A: Let's sketch the graph of the following function:                                       y=2x…

Q: 3. х %3D у* — 2у3 2y3

A: We can find the answer as below using delta method

Q: X-2 %3D

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Q: For what theta value is implemented for the derivative max at point (2, -3) of the function f (x) =…

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Q: 12. f(x) = ( cosx 1+sinx)

A: f(x)= (cosx/ 1+sinx)2

Q: 4 Find the derivative of f(x) using first principle %3D 3x2-3 of differentiation.

A: