Q5: a. Find the mixed partial derivatives for the following function. w = e* + x In(y) + y In(x)

Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

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Q: Consider the function: Which of the following is a partial derivative of this function? x* - Bxy + z…

A: The given function is:f(x, y)=3xye8x2-8xy+12y2

Q: For all functions find the second-order partial derivatives. In each case, show that the mixed…

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Q: Problem 3: Canonical Form (the opposite of problem 2 dx Transform = Ax into one ODE of higher order.…

A: Given dxdt=Ax where A=0100001000011234   To Transform: Given system into an ODE of higher order.

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: Find y as a function of x if

A: The given differential equation y'''-4y''-y'+4y=0D3-4D2-D+4=0D+1D-1D-4=0D=-1, 1, 4

Q: 1-Find the mixed partial derivative: w = e* +x In(y)+y ln(x)

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Q: (늘 가 G-2). Find the value. A relative extrema of the function f occurs at f(x, y) = 9x2 + 3y2 - 9x +…

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Q: Find y as a function of x if x²y" +5xy - 12y = x², y(1) = −9, y(1) = 9. y=

A: We have to find as a function of .

Q: Q3: Use Chain Rule to differentiate the following functions 1. f(r) = (4x² - 3r + 2) 2 2. y = csc(4…

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Q: Let f be a function that is defined and differentiable on all of R. Here is some information about /…

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Q: Q6. Find the first derivatives by using chain rule of the following functions: i. f(x) = tan %3D ii.…

A: Given that:                       (i) f(x)=tan1x(ii)g(x)=lnx3+x-1

Q: f(x) is a function with the domain (-00, -7) U (-7, 3) U (3, 0), and the graph of given below (1.e.,…

A: Given, fx is a function with domain -∞,-7∪-7,3∪3,∞ and the graph of f''x is

Q: B3. (a) Let y be a function of x, defined implicitly by the equation x?y + y3 + x = 0. Find the…

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Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

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Q: For each part of this problem, state whether or not it is possible for a function f of two variables…

A: Answer

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: 8. (a) Using the following table of values for the function f(r, y), determine whether each partial…

A: Step:-1 As we know fx =limh→0 fx+h, y -fx, yhfy =limk→0 fx, y+k -fx, ykfxx =limh→0 f x+2h, y -2…

Q: fand g are the functions whose graphs are shown, y = f(x) is in black and y=g(x) in red. Define H(x)…

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Q: 2x Let f (x) Then the derivative of f is 1 + 4* f'(x) = A(1 + 4*) – Bx(4*) In C where (1 + 4*)D A =…

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Q: I. Find y', y" and y"" of the following functions. a. y = 2x-x'+ 5 b. y = (r²+2) x-1 II. Use the…

A: I. (a).y=2x4-x3+5diff w.r.t xdydx=2(4x3)-3x2+0y'=8x3-3x2diff w.r.t x…

Q: 3. Find the second derivative of f(x) = 2sin²(3x) а. 36сos? (3x) — 36sin? (3x) b. 36сos (3x) —…

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Q: When would you use a partial derivative? When you only need to differentiate half of a function. O…

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Q: Consider the following function which is defined for all x and y: ƒ(x, y) = 2(1 − p²)x²y² − x² - y²…

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Q: 5. Sketch the graph of one function f(x) that has all of the following properties: a.) f(-2) 0 b.)…

A: As per our guidelines we are supposed to answer  only one question. Here question 5) answer.

Q: 2. Find the derivatives: (a) f(x)=(x² - 2x+1) (x² -1) x+2x+5 (b) f(x): %3D x² +1

A: Part (a) Given a function Using product rule of the derivative