The Dirac-delta obeys for any function f(x). a) Show that ro'(x) = −8(x). S f(x)6(x) dx = f(0) b) The Heavyside step function is defined as follows Show that H'(x) = 8(x). H(x)= = 0 1 if x < 0 otherwise.

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

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Q: If f(x) + x2[f(x)]ª = 18 and f(1) = 2, find f '(1). %3D f '(1) =

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Q: Consider the function h(x), for which h(2) = − 1 and h'(2) = -6. Find f'(2) for the function f(x):…

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Q: dx -= In(F (x))+C. What is F (/3) if C=0? For (x+x³) (xtan-'(x) + 1)

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Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: Consider the function f(x), for which f(0) = 4 and f'(0) = -11. Find h'(0) for the function h(x) h'…

A: The function fx satisfies f0=4 and f'0=-11. We have to find the value of h'0 for the function…

Q: 3 X 1 2 3 4 5 f'(x) 5 12 4 3 g'(x) 3 245 1 [3f(x) - 4x] x=3 =(Type an integer or a decimal.) www

A: We will find the required.

Q: 1. Find f'(x) for f(x) = ln x + 2e - 3x².

A: The given function fx=ln x+2ex-3x2. We have to find the derivative function f'x.

Q: 4 given that g(2) = 1 and g'(2) = – 5, what is F'(2)? If F(x) = %3D g(x)' %3D

A: Given, F(x)=4g(x), g(2)=1 and g'(2)=-5We need to find F'(2)

Q: = 2. Find f(x) if f'(x) = 7//1 – x2 and f f(x) |

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Q: Evaluate f'(x) at x =2 given f(x)= (x²– 3)“

A: The given function is fx=14x2-34. Evaluate the differential of function at x=2.

Q: 1. Determine f'(x) for each function below: f(x) = x2 – 2x + 3 f(x) = 7x3 · Vx %3D f(x) = x³ In x…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: if f(x) = x² √In x² x . find the derivative of this function f'(x A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: if f(x) = %79.1 x²√In x² x -. find the derivative of this function f'(x) A. f'(x) = - 1 3:16 1-In x²…

A: The given function is; f(x)=x2 sqrt(ln x2)/x.

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: Let f(x) = z and g(a) = f (2). Find g' (x) by findingf (x) and then taking the derivative. O g' (x)…

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Q: 2x-3 3x (x-3)2 find the x-value(s) where k'(x) is (are) undefined. If k' (x) : for all x in the…

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Q: Suppose g and h are functions such that g (x) = ln (1 + h (sqrtx)). Find g'(4), given that h'(2) = 1…

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Q: The function f(æ) can be approximated by L(x) = 3 – 2(x – 4), near x = 4. What is the value of f'…

A: topic -linear approximation

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

Q: Evaluate f'(x) at x =2 given f(x) = (x² – 3)ª A B 2 © 1 none of the given choices E 4

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Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: Let P(x) = F(x)G(x) and Q(x) = F(x) where F and G are the functions whose grap G(x) y F 2 -1 4 8.…

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Q: x2 with g(1) = 2 and g'(1) = 3. Find the value of f"(1). Suppose that f(x) = g(x)

A: Explanation of the answer is as follows

Q: If f(x) = f'(2) 3x + 1 x + 1 then:

A: given  f(x)=3x+1x+1dxndx=nxn-1d dx(ab)=b(dadx)-a(dbdx)b2

Q: x/f(x) 10. Given h(x) If f(2) = 9, f'(2) = 4, g(2) = -1, g'(2) = -3, calculate h'(2). g² (x)

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