1. Find the gradicnt of the following functions (here, i = V-1, and A is a constant) (a) f (x) = 3x. (b) ƒ (x, t) = 4c*² + 7t². (c) ƒ (z) = 623 (d) ƒ (2) = Acikz (e) f (x, y) = Ac k(x²+y²). + 7.

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: For the function f(x) = Vx – 3. What does (f-1)'(6) = (f-1)(x) =

A: The function is fx=x-3.   Differentiate the function with respect to x. ddxfx=ddxx-3f'x=12x-3…

Q: Find f. f'(t) = 2t – 2sint, f(0)=7

A: From the given problem: f't=2t-2sint And f0=7

Q: dy dx (b) y = (x³ - 2x + 8) (x² + 4) 1. Use the Differentiation Rules to find (a) y = 6x³ + 3x√x -…

A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

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

A: Given : ft = t2 + 7t + 35t2 + 6

Q: x () - (-). y (1) J

A: Givenf(t)=sect   We are required to find f''π4

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: Find f. f(x) = 3 f'(x) = √√√x³ + ³√√x + 5ex + sec² x, f(0) = 8 4

A:

Q: Find the derivative of the following functions a) f(x) = 1 + x² + = 160 1x x6 I b) F(X) x4-3x+1 √x…

A:

Q: Let h(x)=√xf(x). If we know that f'(7) = 6ƒ(7), find a value for f(7) such that h'(7) = 4 (a) f(7):…

A:

Q: . Find the derivative of f (x) = (2x – 6(3x²+8). A. 30x4-54x2+32x %3D

A:

Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

A:

Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Given: fx=ex2, x=0, 4, E=0.0002 To find: n To find: Approximate integral.

Q: 2 For the function f(x)=√x² +4, find f''(x). Then find f''(0) and f''(9).

A: Given query is to find indicated derivative.

Q: If f(t) = (t + 7t + 3) (5t? + 4), find f'(t). %3D Find f'(1).

A:

Q: Solve ,  y" - 8y' + 15y=0

A: Given a differential equation, y''-8y'+15y=0

Q: If f(t) = (t + 5t + 4) (2t² + 2), find f'(t). Find f'(3).

A:

Q: If f(t) = (t² + 6t + 7) (7t² + 4), find ƒ'(t). Find f'(2).

A: INTRODUCTION A function's differentiation can be used to display the rate of change of a function at…

Q: (b) A poll commissioned by a politician estimates that t days after he makes a statement denegrating…

A: Given, S(t)=75(t2-3t+25)t2+3t+25 (i) Approval Rate,…

Q: Consider the function h(z), for which h(4) = -12 and h'(4) = -7. %3D h(z) Find f'(4) for the…

A: To Determine: find f'4 Given: consider the function h(x) for which h4=-12 and h'4=-7 also…

Q: Differentiate the function. ((5y + 1)3 Vy2 + 1 G(y) = In G'(y) =

A: Solve the following question

Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

A:

Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

A:

Q: a. The f'(3) for y = v2x² + 7

A: Since, y=f(x)=2x2+7 -(i)Differentiating equation-(i), with respect to 'x', we…

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: Given f(x) = x + 4, x < 0. Find (f-1)' (5) 10 1 2 | 29

A:

Q: Find y as a function of if y(0) = 19, y'(0) = 19, y"(0) = 4, y"(0) = 0. y(x) = y(4) 4y" + 4y = 0,

A: y(4)−4y′′′+4y′′=0y(0)=19,y′(0)=19,y′′(0)=4,y′′′(0)=0

Q: Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph…

A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

Q: 6. FinD F(S) if f(t)= t· cost

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Q: Find dy/dz y=f(z) (2x2+3x+1) where f(z) is a general function and z=4x3+2

A:

Q: f(3.8) - If we knew that f"(x) < 0 on the interval (3.5, 4.5), would your estimate above be an…

A: We need to find f(3.8)

Q: If f(t) = (t + 3t + 6) (4t² + 3), find f (t). Find f'(3).

A: