3. For the function f(r) = cos(x) find V}(0,27).

Q: (a) f(x) = F(x, 2): then ƒ'(x) = (b) f(x) = F(4,x): then f'(x) = (c) ƒ(x) = F(x,x): then ƒ'(x) = (d)…

A: Total derivative of function z = f(x, y) is given as dz=∂z∂xdx+∂z∂ydy We are allow to solve first 3…

Q: Differentiate the function. 8 + sin(t) f(t) cos(t) (a) f'(t) = Find f'(T). (b) f'(1) =

A: a:Here, f(t) =(8+sin(t))/cos(t)The derivative of f(t) is calculated as follows:

Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

A:

Q: Find and sketch the domain of the function.

A: The objective here is to find and sketch the domain of the given function: sin-1x+y

Q: Given f(x, y, z) = 4 sin(x + y), find f, -3 -3 and f. -3 2

A: f(x,y,z)=4sin(x+y) we simply replace value of x , y and z

Q: =[in(4-x cos (r4

A:

Q: If the slope of the curve y =f-(x) at (4,9) is . 2 find f'(9). f'(9) = 3 (Simplify your answer.)

A:

Q: Consider the function f(x) = sin(4x). a. Determine f '(x). b. Determine f"(x). c. What is the…

A:

Q: Let f (x, y) = 3y O 1 x/3 1/(3у) (1/3)y

A:

Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(n/2) = 6. %3D %3D f(x) =

A: We have to  solve

Q: -y . If f(x, y) is harmonic, show that f is x2 + y2' x2 + y2 also harmonic.

A:

Q: 8. Find f(113) (x) for f(x): = COS X.

A:

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.