. Suppose that your best friend has calculated the partial derivatives of a given function f(x,y) and told you that fa(x, y) = 2x+3y and that fy(x, y) = 4.x+6y. Based on sound mathematics, would you believe your best friend? Why or why not?

Q: Differentiate the followings. (x+ (i) y =

A: If given an expression of a function which is a multiplication of two separate functions. In order…

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

A:

Q: The equation of then tangent line to y?e2* = 3y + x2 at (0,3) is y= – 6x + 3 A) True B) False

A:

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

A:

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: Find f, (2,0) if f(x,y) = 18x e Y. 1,(2.0) = %3D

A:

Q: 6. Given that f(x,y) = xin y, determine fy(x, y).

A: The given function f(x,y)=xsin y

Q: If f(x.y)= x?+2xy+5y² then дудх

A:

Q: f(x, y) = 8 – + xy. I y

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 f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: If f(x, y, z) = 2x5 + 3y5 - 8x3y²z², what is the partial derivative of f with respect to x? (A 10х4…

A:

Q: I. Find the derivatives of the following functions: 4. -3xy? + 5x²y² = 2x² %3D

A:

Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

A:

Q: Find the derivative of the function at the given point in the direction of A. f(x.y,z) = In (x…

A: Solved below.

Q: Q5.Find the first and second derivatives of the following functions with respect to the given…

A:

Q: In the next exercise you have to equal the derivative to zero and then clear x or a y to subtract in…

A:

Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

A:

Q: for the function below f(x, y) = 5xy – 7x² – y² + 3x – 6y + 2 Partial Derivative for y = %3D 5x- 7у…

A: