y = In(x + 2) at [-1,2]

Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Find the derivative of the function f (x, y) = x²y + y²z: at Po(1,2,3) in the direction of û = 2î –…

A: To find the derivative of the function f(x,y)=x2y+y2z at P0(1,2,3) in the direction of…

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 +…

A:

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

Q: Find all the second partial derivatives. f(x, y) = x³y² + 6x^y fxx (x, y) = {xy(x, y) fyx(x, y) (xin…

A: We want to find second order partial derivatives.

Q: The integrating factor of the LDE y' = x - 2ycotx is

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Q: Differentiate ysin(1/y)=1-xy

A:

Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

A:

Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: Expand x'y + 3y - 4 about the point (1, -2) by Taylor' s theorem.

A: Let, the given function be fx,y=x2y+3y-4 and the given point is 1,-2

Q: If f(x, y, z) 2x5 + 3y5 - 8x2y2z2, what is the partial derivative of f with respect to z?

A: The given function is fx, y, z=2x5+3y5-8x2y2z2.

Q: Find the partial derivative of f(x,y) = 5x3y2

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

A:

Q: Find the requested partial derivative. dz z= (3x +4y) ; (2,5)

A: Option D is the correct option. Use the chain rule to find the partial derivative for z w.r.t x.

Q: Find the partial derivative. z = (2² + 2x – 6y)"

A:

Q: What is the mixed, second order partial derivative of this function. f (x, y) = / 2x² + y²

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Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: Write the equation of the tangent line to f(x) = + In(a²) - 4 at x = 1. O y = 3x - 6 Oy = 4x - 7 Oy…

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Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

A:

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Find all the second partial derivatives forf (x, y) = x³y5 + 2x*y.

A: All the solutions are given below.

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: Find the first partial derivatives of the given functions. z = x3 - xy? + 3y?

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Q: Find the partial derivative. = (a² + 4x – 2y)° - dz II

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Q: Find the linearization of ƒ(x) = √1 + x at x = 0

A: Consider the following function: fx=1+x Differentiate fx with respect to x: ddxfx=ddx1+xf'x=121+x

Q: Find all second partial derivatives of the function f(x, y) = In(3x? + 5y).

A:

Q: Find all second order partial derivatives of f(x, y) = 6x²e3y

A: Consider the function fx,y=6x2e3y

Q: Find the second-order partial derivative fxx ( x , y ) of the function f ( x , y ) = x 4 y 4 - sqrt…

A:

Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Find the first partial derivatives of the funct f(x, y) = x8 + 7xy5 fx(x, y) =

A:

Q: Find all second-order partial derivatives for ƒ(x, y) = -4x3 - 3x2y3 + 2y2.

A: To find all second-order partial derivatives for f(x,y)=-4x3-3x2y3+2y2.

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

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Q: Find Zxx=Zyy=Zxy=

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Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

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Q: 3z2+x 30. If z – xz – y = 0, prove that- =- ax dy (3z²–x)³*

A: Let's find.

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

A:

Q: Find both first partial derivatives. z = 6x − x2y + 8y2

A: Find both first partial derivatives. z = 6x − x2y + 8y2

Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

A:

Q: Find both first partial derivatives. z = x2e2y

A: Given function is z=x2e2y. Partial derivative means derivative of function with respect to one…

Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: Find the 1st partial derivatives of z=(4x+6y)^11

A: Here we have to find partial derivatives by differentiating it with respect to x ( keeping y…

Q: End fz(3) in terms of the joine pdf of X and Y if

A: From the given information, Let, f(x) be the density function of X. f(y) be the density function of…