f(x) a) h'(2) for h(x) = b) k'(4) for k(x) = g(f(r)+r). [Hint - You'll need to use the chain rule with f(x)+{r as your inner function].

Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: Find the derivative of f(x) = (3x – 2x?)’using the chain rule %3D

A:

Q: If U = lx+my,v=mx-ly then prove that partial derivative of x

A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: 5. Find the first partial derivatives of w= In(x+2y+3z) %3D

A: The given function is w=lnx+2y+3z

Q: Use the limit definition of the partial derivative to verify the formulas

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: For z = arctan(x² + y²): Compute all first and second order partial derivatives. Find the…

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Q: Vz²+1 ev° dy In a

A:

Q: Find partial derivatives of x3sin y + cos2x tan5y with respect to x and y

A: We have to find the partial derivatives of  x3siny+cos2xtan5y with respect to x and y.

Q: Find the first partial derivatives of the function. z = (7x + 8y) az !! ax %3! ду

A:

Q: Differentiate implicitly to find the first partial derivatives of z                              x2…

A: Given that function, x2 + y2 + z2 = 1 Differentiate with respect to x on both sides,…

Q: Differentiate implicitly to find the first partial derivatives of z…

A: the given implicit function is:xlny+y2z+z2=8

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: Find the value of ∂x/∂z at the point (1, -1, -3) if the equation xz + y ln x - x2 + 4 = 0 defines x…

A: Given equation is xz+ylnx-x2+4=0. Given point is 1,-1,-3. Partial derivative of given equation with…

Q: Differentiate implicitly to find the first partial derivatives of z. 11x2 + 5y2 + 3z² = 100 az əx az…

A: Given,  11x2+5y2+3z2=100

Q: The partial derivative fx(-1,0) of ƒ(x, y) = xe³ + x² + 1 is equal to −1. Select one: True False

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Q: Find the first and second order partial derivatives for z x2 sin (3x + 2y).

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Q: I need help finding all of the first order partial derivatives for the function

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Q: Differentiate implicitly to find the first partial derivatives of z. 7x² + 3y² + 11z² = 36 əz əx əz…

A: Differentiate implicitly to find the first partial derivatives of z.   7x ^ 2 + 3y ^ 2 + 11z ^ 2 =…

Q: If f(x) = Α) B C D tanx sec ³x 1 + e tanx 1+tan²x 1+ e tanx sec²x 1+1² 1+e' -dt, then f'(x) equals…

A: We have to find derivative of given integral.

Q: 4+2x If g(x.y) = By then the mixed partial derivative at the point (- 2. is:

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Q: Determine the indicated (in the attached image) partial derivative of z = x4y5 - cos(x3y2)

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Q: Find both first partial derivatives. z = 4y²/x az ax az ду || ||

A: z=4y2x

Q: Find both first partial derivatives. z = 2y2√x

A: fx = differentiate with respect to xfy=differentiate with respect to yddxxn=n xn-1

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: How do you remember the methods for partial derivatives in the chain rule for several variables?

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Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: Compute the partial derivative of h(x, z) = e4xz-3x²z. (Use symbolic notation and fractions where…

A: In this problem first we need to partially differentiate the function with respect to z and then put…

Q: Differentiate implicitly to find the first partial derivatives of z. 7x2 + 5y2 + 2z2 = 25 az ax dz

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Q: Use the Chain Rule to compute the partial derivative. би +о In (3u? + uv) = 3u + uv

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Q: Find the first and second order partial derivatives for z = x² sin (3x + 2y).

A: As we know that; The product rule: f·g'=f'·g+f·g' The chain rule: fgx'=f'gx·g'x And The first order…

Q: Compute the partial derivative In(x² + xy).

A: ∂ ∂ xlnx2+xyTreat y as a constantApply chain Rule,∂ ∂ xlnx2+xy=1x2+xy∂ ∂ xx2+xy                    (…

Q: Find both first partial derivatives. z = In əz əx az ? ду II

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

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Q: Find both first partial derivatives. z = cos(x2 + y2)

A: Given , z=cos(x2+y2)we have to find the first partial derivative

Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

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Q: Compute the indicated partial derivative. g(x, у) %3 сos(x + ) 9xxy

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Q: Find all first partial derivatives. z = ln(x2 + y2 + 1)

A: Given The equation is  z = ln(x2 + y2 + 1) .

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Consider the following function: fx=x2+2x Differentiate fx with respect to x: ddxfx=ddxx2+2xf'x=2x+2

Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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

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Q: 2) Use the Chain Rule to express the second derivative of ƒ • g in terms of the first and second…

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Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

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Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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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 derivative of f (x) = In(3x² – x)³ in two different ways; (a) with the chain rule %3D | and…

A: Given fx=ln3x2−x3aUsing Chain Rulelnfx'=1fxf'xDifferentiate w.r.t…

Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

A: