Find the total derivative of f(z, y) = xy+3y² is a. df = ydx + dy b. df = ydx + 6edy C. df (a +y)da + 6ydy d. df = ydx + (x + 6y)dy

Q: Which of the following is the derivative of y +3x ? Select one: dy a. da 3x 3 dy b. dz = 3x? dy C.…

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Q: f(x,y) = e (3x² + 3y2)

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Q: d_(F(x*)) d dt dx dx 16

A: To find- solve the given equation.

Q: Differentiate f (t) = 4e0.05t - 23e0.01t

A: Solution  Given the function as,  Use chain rule for exponential function as follows: Also,…

Q: d y. d3y dy d'y dy (+() dy + y dt2" dt + b dt dt2 ay dt3 d/dt (5 %3D dt

A: Explained below

Q: Find and sketch the domain of the functions of two variables: 1. f(x, y) = = 16x² - y² x + 3y

A: The given function is  fx, y=16-x2-y2x+3y We have to find and sketch the domain of the given…

Q: dy of the function: dx Find the derivative Зx3 — 4x2 + 5 + Vx- 2Vx5 y = | x2

A: The given function is  y=3x3-4x2+5+x3-2x5x2y=3x3-4x2+5+x13-2x52x2

Q: Find the second derivative, Select the correct answer below: d² 9x² dx² y³ d²y 7.3 dx² 3y³ d²y dx²…

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Q: d²y d²y dy + d dt. d dy dy = ay + by dt dt. dt dt2 dt2 dt

A: We find the value of a,b,c and d.

Q: Find the derivative of the function at the given point in the direction of A. f(x, y) = -10x2 + 5y,…

A: This question is related to directional derivative of a function, we will solve it by finding…

Q: Find the relation of the derivative of y and y with respect to x, given that yx-y? = 3x 3x II. 1-2xy…

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Q: f(x) = V5 + v6x. Find f '(x).

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Q: Find the derivative dy if y(x)- Vx+1 dx dy xp dl (O

A: Given:

Q: Use the quotient rule to find the derivative. x² + 8x +3 y= √x OA. dy 2x+8 dx X B. O C. dy dx dy dx…

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Q: (m) y = f (n) y = f x +3 V1-x² dx x² + 10x + 30 2 -dx.

A: Solve the following

Q: Evaluate f(f(x+2y)dy) dx.

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Q: Normalize (z) = 3f2(x) +2f3(x). You can think of functions being 0 beyond the [0, L] interval, where…

A: Simple Linear Scaling:If f2(x) and f3(x) are linear functions that map the [0, L] interval to [a, b]…