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

Q: If f(x) 3 find f'(2). x²

A: Given that f(x)=3x2So, f(x)=3x-2

Q: f"(x) = 24x2 + 2x + 8, f(1) = 2, f'(1) = -2 f(x) =

A: given that f"x=24x2+2x+8, f(1)=2 and f'1=-2 find f(x)

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).…

A:

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

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

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=…

A:

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

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

A:

Q: Differentiate. f(x) = In In dx (5x + 2)(x+7)3 (1-6x)6 (5x+2)(x+7)3 (1-6x)6

A:

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

A:

Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

A:

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

A:

Q: 6. (a)f dx x(x +3)2

A: To evaluate the given integral

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

A:

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

A:

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

A:

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: f(x)= if'(-3)

A: The differentiation is a process of finding the rate of change of one variable with respect to…

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: 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:

Q: Find f. f(x) = f"(x) = 6 - 6x - 40x³, f(0) = 5, f'(0) = 7

A:

Q: etermine the equation of your model that will pass 2,4

A: We already have the equation of polynomialand

Q: 5x +2 Q5. If f(x)=: 3x -x then find f'(2)

A:

Q: Let f(x) = ( – 2° + 2)* (5æ² + 4)" f' (x) =

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.