Let r(x) = f(g(h(x))), r'(1) = where h(1) 2, g(2) = 3, h'(1) = 4, g'(2) = 5, and f '(3) = 6. Find r'(1).

Q: Find both first partial derivatives.

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

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

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Q: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

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

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Q: Find both first partial derivatives. . z = ln x/ y

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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: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

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Q: In(x), Sn (4t + et) dt. Find the derivative of F(x). 3.

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Q: Find the partial derivative fx ( x , y ). f ( x , y ) = x ln ( 3x + 4y )

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: 2. use the fundemental derivative formula to differential the folwing at x=2 • gex) = 3x-1 2メ+1 (1o…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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

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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: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

Q: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

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Q: derivative

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Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

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

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

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A: Use formula of derivative to solve

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

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Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: (b) Find all first and second partial derivatives of z = x² In(x² + xy).

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

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

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

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Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.

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Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: Find both first partial derivatives. z = cosh xy2

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

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

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Q: Find both first partial derivatives. z = x2e2y

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Q: (or axay дудх Calculate the second-order partial derivative of f(x.v) = xy with respect to x and y,…

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Q: Find the derivative of the function. 4x - 5 8x + 1 dx dx d (8x + 1) • (4x - 5)– (4x – 5) • d (8x+1)…

A: Explanation of the answer is as follows

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

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