We now turn our attention to functions of two or more variables. For example, the formula f(x, y) = x'y3 defines a function that gives us one output for each pair (2, y) which we input. If we plug in a = 2 and y = 1, we get f(2, 3) = (2) (1)° = 4 ·1 = 4. If we plug in x = 3 and y = - 1, we get f(3, – 1) = (3) (- 1)° = 9 - (– 1) = – 9. And there are infinitely many more points of the form (x, y) which we could input into f. %3D Using the same function f(x, y) defined above, evaluate the following expressions: f(1, 3) = f(2, 2) = f(- 2, - 2) = f(50, 0) =

Q: 3. y = xVx 4. у%3D 3x2 - 5x+2 5. у%3-14х-10

A: Use the formula ddxxn=nxn-1 1. Given function is, y=4x3. Now, differentiate this function with…

Q: 1) BASIC DERIVATIVES: Differentiate and simplify the following functions a) f(x) = 5x³+3x² - 5x+2 b)…

A: We know that the derivative of x^n Is  nx^(n-1)

Q: 6. A liquid starts at a temperature of 190 F and cools down in a room held at a constant 65 'F.…

A: NOTE: Refresh your page if you can't see any equations. .  room temperature = 65 initial…

Q: Find the derivative of the function. y = Xx x + 3

A:

Q: The equation of motion of a particle is s = t-5t, where s is in meters and t is in seconds. Assuming…

A: Please see the below picture for detailed solution.

Q: Your name is Francesca Dragonetti (an assistant of Galileo Galilei) and, to impress your boss, you…

A:

Q: Question Given where y(0) = 1, solve for y. You may leave your answer as an implicit function of y,…

A:

Q: Ohm’s law says that the current, I, (in amps) obeys the formula I =V/R where V represents the…

A:

Q: A classmate is building a mathematical model for the temperature in his home during the summer. He…

A: Given function is: Th=-12cosπ12h-1+75 where T is degree in Fahrenheit and h is the number of hours…

Q: The reaction of the body to a dose of medicine can sometimes be represented by an equation of the…

A: Use product rule for differentiation

Q: Differentiate the following functions: Chain Rule

A: NOTE: Refresh your page if you can't see any equations. . take derivative apply chain rule

Q: Find all points at which the direction of fastest change of the function f(x, y) = x² + y - 4x - By…

A:

Q: Find the third derivative of the following function: f (x) = 10x³ (x + 20) 240x + 1200 dæ3 240x +…

A:

Q: v 1. y = x³/2 ? v 2. y = 2/(x³) v 3. у 3D 14x12 ? v 4. y = 3x' + 2x? 5. у 3D 12. 14* ? 6. y = V4x4

A:

Q: According to Newton's Law of Cooling, the temperature T of an (as a function of time t) is given by…

A: Given, T(t)=Ts+D0e-ktwhere k=0.05

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.