1. Find f'(x) of each of the following functions x²e¬x f(x) : x+1 2x+1 f(x) = Vx2+3 ' f(x) = In. x+1 f(x) = e** In(x³). %3D

Q: Find f. r'(x) = Vx(3 + 10x), (1) = 11 (x)

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Q: find the function f(x) if f'(x)=(2/1+x2)+(5/7)x5/7 and f(0)=2

A: Given, f'(x)=(2/(1+x2))+(5/7)x5/7

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: If f(x) = 10x + 4, find ƒ'(10). f'(10) =

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Q: If f(x) = (3x +8) find f'(z). Find f'(1).

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Q: Find f. f'(x) = 12x - 12+ x > 0, f(1) = 1 %3D f(x) =

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: Compute and interpret f'(1) for each function above. f(r) = 6x2 + 3x 4 f'(1) = %3D

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

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Q: (2-9x³), find f'(x). Given f(x)= In (2-9x³), f'(x) =

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Q: Find f'(x) and f'(c). Function f(x) = (x³ + 4x)(7x² + 5x − 6) f'(x) = - f'(c) = = Value of c 0 = 5

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Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

Q: Consider the following function: Step 1 of 4: Determine ƒ'(x) and ƒ"(x). f(x) = (x − 1)(x+8)² Answer…

A: Step 1:To determine f′(x) and f′′(x) for the given function f(x)=(x−1)(x+8)2, we can use the product…

Q: If 11 +3f(x) + 8x²(f(x))' = 0 and f(1) = -1, find f' (1). f'(1) =

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Q: Let f(x) = x + 12 f-'(x) = %3D 1.

A: Let's say y = f(x) A function g is said to be inverse of a function f, if g(y) = f(x) Procedure to…

Q: Find f. f"(x) = -2 + 36x - 12x2, f(0) = 2, f'(0) = 18

A: Given, .Given,  f(0)=2, f'(0)=18.We know,

Q: If f is the function f (x) = + 4/x, then f' (4)

A: The function is  f(x)=4x+4x

Q: Find f. 3 f'(x) = 1 - x? f(x) =

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

A: Write the given function using exponent.

Q: Find f. f(x) = f"(x) = -2 + 18x - 12x², f(0) = 3, f'(0) = 12

A: Integration

Q: Find f' (x), if f (x) = 3Vx + 2Vx – 11 %3D

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Q: Find f. f"(x)  =8  x3 + 5   , f(1)   =  0 , f'(1)  =8

A: It is given that, f''x=8x3+5,  f1=0, f'1=8.   Integrate the function f''x=8x3+5 as follows".…

Q: Find f '(x). f0) = (+4)5 f(x) f '(x)=|

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Q: 3. Let f(x) = 4x3+ + 2vx-7. Find f'(x).

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Q: If f(x) = x2 - Vx + 2, find f'(x). %3D f'(x) = %3D

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Q: |x-3. Find flexo :)? f(x) = \ / . \

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Q: Find f. 4 f'(x) = 1- Ex) = %3D

A: This is a problem related to integral. Based on the given differential equation we will calculate…

Q: Let y= f (x) be a function with f (4)=12 and f(4)= 0.5.

A: We have to find

Q: Find f. f"(x) = -2 + 36x – 12x², (0) = 8, f'(0) = 18 "(x) =

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Q: F(x)=-4cosx-9tanx , f’(4pi/3)= ___

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Q: Differentiate the given function: f(x) = In(2r³ – 5æ) 6x² – 5 A f'(x) = 2x3 – 5x 1 ® f'(x) = 2x3 –…

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Q: Differentiate the following function. f(x) = 6 +5x+4ex f'(x) =

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Q: 2 Determine f'(x) given f(x) = (2x + 4)? • Vx. %3D

A: fx = 2x+42×xApply chain's rule ,f'x = ddx2x+42×x +2x+4ddxxf'x = 2×2x+4×d2xdx×x +2x+4×12xf'x =…

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.