Q1 (a) Find the first order partial derivative in terms of x and y of the function f(x,y,z) = xy²z³ + esin(x³y²z)x² – y³ + z – 7 (b) Hannah Delisha received a square based gift box without a lid. If 90 cm? of material is used, determine the maximum possible volume of the box. Determine the local extreme value of the function f(x, y) %3D 2x? — уз — 2ху + 4

Q: two Q2A: Find the first order partial derivative of the following three variables function: y u…

A:

Q: The cost (in dollars) of manufacturing one item is given by C(x, y) = 70 + 4x + 9y where x is the…

A:

Q: z = x3 – xy? + 3y2

A: Let us consider the two variable function z=f(x,y) The first partial derivative of the function is…

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Explain in a sentence what the partial derivative of f with respect to x represents in the context…

A:

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: Both first partial derivatives of the function f(x.y) are zero at the given points. Use the…

A:

Q: Consider the function f(x,y)=x²e*-7x²+x+3y-2. Calculate the partial derivative fx(1, 2). Answer:

A:

Q: The total derivative of the function ƒ(x,y) =2x²y– xy is df = (2x² – x)dx +(4xy – y)dy b. df = (4x –…

A: df  = (df(x,y)/dx)dx + (df(x,y)/dy)dy f(x,y) = 2x^2y - xy df(x,y)/dx = 4xy - y df(x,y)/dy = 2x^2 - x

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

A:

Q: Q. 6. Consider f (x) = -* + 2x + 1. x3 3x2 3 Use derivatives to separate the regions where function…

A: If f′(x) > 0, then f is increasing on the interval,and if f′(x) < 0, then f is decreasing on…

Q: Find the derivative of the following functions: (Do not simplify) A.f(z) =E B. g (포) %3Dz In(5x? +9)…

A:

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: (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: 6. Use the quotient rule to find the derivative x - Vx y x + Vx (а) 8x2+ 2x y = x - 1 (b) 4х — 1 (c)…

A:

Q: derivative for this question. I gave the easy function. a) Domain of f(x) is b) Find the…

A:

Q: f(x₁, x₂) = x₁ ln(x² + x² + 1), X = = (x₁, x₂) € R²,

A:

Q: az x²+y² - z² = 2x( y + z) ; 江一下

A: