If f(x) = X S 1.² (2.3 (+³ 0 then f"(x) = || + 5t² + 7) dt

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: Given the function below f(x) = 3 x³ – ²x² − 18 x + 3 a) Differentiate the functionƒ(x) = 3 x³ − 2…

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Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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Q: Consider the function Compute f"(x). X = 66²⁰ - f(x) = -3t²- f"(x) = -4t+ 3 dt.

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Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx &gt; 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: 2 cosh x +losion2x = 5

A: I am attaching image so that you understand each and every step.

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

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Q: Suppose f(x) √₂+² = √1+tdt 2x find f'(1).

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Q: solve the equation :- y'(t) = y(t) [a-y(t) ] ₁ y(0) = a/2, 970

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Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Find f(x) dx if S5 f(x) lx for x 2 5' for x < 5

A: Given- ∫07fxdx if 5    for x&lt;5x    for x≥5 To find- The value of the above integral.

Q: f(t)= 140/3 t^2 + 3000 does concavity for f(t) change . t is in days

A: Given : f(t) = 140/3 t2 + 3000

Q: Solve X(Inx - Iny)dy - ydx = 0 %3D

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Let f(x)=100/5+2e-0.01x. Find f'(x).

A: Write the given function using exponent.

Q: Find the intervals on which the function is increasing or decreasing where f'(x) = 4x³ – 4x.

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Q: Find f'(1) if Aæ) = (x² –-x²-x+1)(x² + 1). 1 O 2 O -3

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Q: If f(4) 8 and f '(x) 2 1 for 4 < x < 9, how small can f(9) possibly be?

A: Given:- If f(4) = 8 and f '(x) &gt; 1 for 4 ≤ x ≤ 9 To find:- How small can f(9) possibly be?

Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: Differentiate the following function. = VP + 2V7 u = u'(t) =|| I

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Q: If f(t) = (t² + 3t+2) (5t² + 4), find f'(t). 201³ + 45t² + 32t Find f'(2). 40 X

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Q: d²y Find the second derivative (Notation: 2 or y') if xy = y² + 2. Simplify dx² until there are no…

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Q: Find f(x) dx if S2 for x 2 Neod Heln2 Telk te a Tuter

A: To find the integral of the given function.

Q: What is the first derivative of f(x) = √√x² + 2x − 1?

A: Given the function,    fx=x2+2x-1

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: 2x 5. F(x) = "(5t – 1) dt

A: Here, it is given that F(x)=∫x2x5t-1dt

Q: Let f(x) = 9 + V2x - 9. Find f(r).

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Q: The derivative of x at X = 1 is to I Frue or false 2

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