2) i)' If 1 [ f(x) f(z)dz = 6 ln(|z|) sin(z) - 3e³ +2². then find f(x). ii) { Evaluate se - r² + 16x + 8 2x -)dx +6x + C

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: Find the derivative (df/dx) 1- f(x) = cscx - 4√x + 7y−² 2-f(x)=x² cotx-x-2 3-f(x) = (secx + tanx)…

A: We have to find derivative of given function.

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: f(x) = ln[x(x + 6) 5 (x²+2)4] f'(x) =

A:

Q: 2. (a) Find the derivative of f(x) = 2x2 – 2x + 2 from first principle sin x (b) If y = x + find x4…

A:

Q: Step 3 Now write the derivative in terms of x by recalling that u = -3x + 7 and v = x + 7. du 1 +=…

A:

Q: 1) The distance, travelled by a car, f(x), in meters, after x hours, can be represented by f(x + 20,…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: find the derivative, show all work please. f(x)=square root(4x2-2x+3)

A:

Q: 9. f(x)=T √√5x²

A:

Q: Find the third derivatives of the function f (x) = e sin (2x)

A:

Q: x+3 4) Evaluate f dx x+1

A:

Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

Q: 3. Find f'(x) for f(x) = 3x-4 2x+3

A:

Q: f(x) COSX f'x) 2.

A:

Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

A:

Q: a) y = −8x² + 4x¯¹ − 2 b) f(x)=√√x - √x 5 c) g(x) = x³

A:

Q: B. Find f(x) if f

A: Solution of the problem as follows

Q: Iff (x) = x sinx, thenf' (x) = ? O xsin(2 + x) O 2rsinx O xcos(2 + x) O 2xsinx +xcosx Oxcosx

A:

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

A:

Q: and assume f(-2) =0 f'(– 2) = - 1. Find h'(-2). Let h(x) =x²e*(x)

A:

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: First derivative of ₂ F₁(x): d a {2 F₁ (a, b; c; x)} = dx a.b с 2F₁ (a +1, b+1; c + 1; x)

A:

Q: Differentiate. f(x) = In (4x+5)(x+8)5 (1-4X)6

A:

Q: Let f(x) = sin(4g(x)). Evaluate f'(x).

A:

Q: 7. Determine f'(x) where

A: Derivative: - The rate of change of a function with respect to a variable is called derivative in…

Q: FIND F'(x) F(x) = 2 tanx 1+cosx

A: To differentiate the given function.

Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: The f ²-3)³ dx is equal to x2

A: Given: I=∫x2-33x2dx For evaluating given integral, first we simplify given expression then integrate…

Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: Step 2: Step 3: Sten 4:

A:

Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions

Q: 24. (EXERCISE) Consider the function f(x)=3x* – 20x' + 42x² – 36x

A: The given function,   f(x)=3x4-20x3+42x2-36x

Q: Let f(x) ƒ'(x) = ƒ'(3) = = √2x² + 4x + 3

A:

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

A: The function given to us is as follows: fx=x+1x2+1 at  x=0, 3 We are asked to find the integral of…