Let g, h: -R and /:R'+ R be defined by /(x, y) = (g(x, y), h(x, y). Assume curl /(x, y) = 7x – 7y, divf(x, y) = 7y – 8x, and Vg(x, y) = (2x – 4, 6y – 6x). Find the h(x,y) =( "(1,-1)%3D

Q: Find f'(a). f)t( 1 t² +4

A:

Q: Find f. 4 f'(t) 1 + t2 f(1) = 0

A:

Q: If you know that f(x) = f'(x) = f"(x) and that f(2) = 3 while f(6) = 3e* then: T. f''(x) dx %3D

A: We have to evaluate the integral ∫26xf''(x)dx. We have given that f(x) = f'(x) = f''(x) and f(2) = 3…

Q: If f(t) = (t + 7t + 3) (5t² + 6), find ƒ'(t). Find f'(5).

A: Given : ft = t2 + 7t + 35t2 + 6

Q: Let f(1) = 1, g(1) = -3,h(1) = 2, f'(1) = -1,g'(1) = 2, and h'(1 d f(x) g(x) dx h(x) Find when x =…

A: Please refer to the image below

Q: Calculate the derivative of the function. f(x) = [(2x – 1)2 + (1 – x)°]? %3D f'(x) = %D

A: We will find the derivative using chain rule.

Q: 50 30 SO then s0 f(x)dx equals? Choose one. ()B-A (2) 2A+2B (3) 2B (4) A+B (5) A-B 16) 0 (7) 2A…

A: To evaluate the given definite integral.

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: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

A:

Q: Find f'(a). 1 f(t) t2 + 5

A:

Q: Let c =8 If f (x) = ecsin(). Find f' (0)

A: Given c=8and f(x)=ec.sin(x)⇒f(x)=e8sin(x)

Q: Find f '(a) f(t)6t12 t 7

A: The given function is

Q: y y=f'(x) 2

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: Find f if f"(x) = 0, f(0) = 2, f'(0) = 1

A:

Q: ex+1 b) Find f'(x) of f (x) = x2+3 %3D c) For y = xk+1, where k is a constant. Find y'".

A:

Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

A:

Q: Suppose F(8) = 5, F(9)= -23, and - 9 f6f (x) d Your Answer: Answer dx= F'(x) = f(x).

A:

Q: Is |3x-1| a function?

A: A relation is said to be a function only when every point in the domain has a unique value in the…

Q: F(s) = Le 4t cos(5t)}

A: We have to find  ℒe-4tcos5t Remember : ℒeatf(t)=Fs-a where  ℒf(t)=Fs

Q: Find f '(a). f(t) =  3t + 9 t + 8

A: Explanation of the solution is given below...

Q: F(x) = 3Jx#6 + K Given find the value of k if f(-3) =19 f'-2) =- 3 ·

A:

Q: If f'(1) = 3e2 and f(0) = 2 then find f(1). %3D %3D

A: Given:     To determine: f(1)

Q: Find f '(a). 8t + 18 f(t) t + 3

A: The function is given as ft=8t+18t+3 Differentiate the above function w.r.t 't' f't=ddt8t+18t+3

Q: Q6/Find the derivative (df/dx) f(x) =+5 e* %3D -4 x-7/3 + 5e* x-7/3 + 5e* O 1, O 2 Fr73 + 6e"

A:

Q: F(x) = Vt² + 11 dt

A: F(x)=∫5xt2+11 dt