1. f(x) = e*+'; '(-1) S(x) = V – 1; f(9) f'(3) *n. f(r) = V7x + 6; "(3)

Q: If f(x) = 8x + 2 x² + 7 find f'(x).

A: In this question, we will find the derivative of the function.

Q: Find f. f ''(x) = 20x3 + 12x2 + 10,    f(0) = 4,    f(1) = 2

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Q: Using the figure below, where f' (3) = 2.1.f' (6) = 3.0,f' (9) = 3.7,f' (12) = 4.2, find (f-1)'(12).…

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Q: Find f'(x) and simplify. f(x) = 2x³ Inx Which of the following shows the correct application of the…

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Q: Differentiate. x2 -9 f(x) = In f'(x) = O

A: Explanation: Given that,  f(x)=lnx2-9x

Q: Find f. f "(x) = 5/ /1 - x2, = 2 ()- 2. f(x) =

A:

Q: Find f. f"(x)  =-2  +12 x -12 x2   , f(0)   = 4 ,f'(0)  =12

A: Given ,f''x=-2+12x-12x2f0=4f'0=12

Q: x-²²-3 ²-3, determine the x-value(s) where f(x) changes from concave up to concave down. f(x)= Ox=…

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Q: f(x)= 3*+log2* Find f'(x)

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Q: Find (f ¹)'(a). (F-¹)(a) = f(x) = 4x³ + 3x² + 5x + 9, - 3x² + 5x+9, a=9

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Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

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Q: Find f'(x) and simplify. x²+2 7x-8 f(x) = Which of the following shows the correct application of…

A: I have explained everything with in the solution. Please go through that.

Q: Given f()= 2x + 1 and ()= r*+ 2x-1, fnd (f- (1).Then valute the difence when x=2.

A: Sum and difference of the two functions

Q: 1-2 h(r) = 1=7²³²₁ 2-3 . Find h' (1).

A:

Q: IF F"(X)=12X^2+24X-6 ,  F'(1)=10,   F(2)=20 , determine the function f.

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Q: r 4-5x 3. f(x)=- ; f'(-1)

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Q: Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values…

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Q: 10) Find (ƒ^¯') (-5) if ƒ(x)= x³ +3x−1.

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Q: Which of the following is the negation of the proportion: "For every natural number n, 2n + 1 > 1."

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Q: D. Check all boxes that apply to the number: a) b) c) d) √81 1.2 0 13 Ei. 78940.7895 Natural Whole…

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Q: 2х + 2 If f(x) find: 7х + 3 f'(x) = f'(2) =

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Q: Find f. f ''(x) = 20x3 + 12x2 + 4,    f(0) = 6,    f(1) = 1 f(x) =

A: According to question,Given Derivative,f''x = 20x3 + 12x2 + 4,f0 =6,f1 = 1

Q: Evaluate the integral. 4 1 dx 2x Ji

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Q: point) If ƒ(5) = -3, g(5) = -4, f'(5) = -2, and g'(5) = -2, find the values of the following: %3D (f…

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Q: find f'(x) for f(x)= (5x-2)3 (1-x3)4

A: It is given that the function is

Q: From the graph of f(x), determine the graph of f'(x). -6 -5 -4 -3 -2 -1 y 6 10. d 3 2 1 O -1 V 2 3 5…

A: Given graph for f

Q: Find f. f ''(x) = 4 + 6x + 24x2,    f(0) = 5,    f (1) = 14

A: To find out the function f whose double derivative and some initial conditions are given.

Q: Find f'(16) if f(x) = 7x² + 3x +3 √I

A: To find the derivative of given function

Q: Find f. f"(x) = 48x2 + 2x + 6, f(1) = 5, f'(1) = -5 %3D

A: Given,  f''x =48x2+2x+6  f'1 =-5 f1 = 5  We have to find fx

Q: If f(x) = 4, find f'(- 11).

A: The given function is:fx=4To find f'-11

Q: f(x) = (x³ + 2x + 7)4 f' (æ) = f' (5) =

A: Consider the given function: fx=x3+2x+74 Differentiate the function using chain rule which is given…

Q: Find f. f"(x) = -2 + 30x – 12x2, f(0) = 8, f'(0) = 16

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.