07 * O O 3 7 0 Exercise 1: If f(x) + g([f(x)]²) = 7. Find f'(2), when f(2)= 3 and g'(9) = -1

Q: For the function f (x) = 5a- 7x +4r + 3 %3D a. Find f '(x) b. Find f" (x) c. Find f" (0) and f “ (2)…

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Q: Suppose that f(x) = f'(2) = -2 x6 Evaluate the following: ←

A: f(x)=-2x6d dx(xm)=mxm-1

Q: Let x + 2 f(x) x + 9 f-(- 9) =

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Q: If f(x) - 5', show that f(x + h) – f(x) 5" h h

A: given that f(x)=5^x

Q: Find f. f"(x) = 4 + 6x + 24x², f(0) = 2, f(1) = 11 f(x)

A: Just integrating given equation twice and then find the value of integration constant with the help…

Q: Find f. f"(x) = 8 + 6x + 24x², f(0) = 5, f(1) = 15 f(x)

A: Find your answer below

Q: 2. L{(2t – 2) U(t – 2)} |

A: We have to find Laplace transform of given function using Heaviside Shift Theorem.

Q: If f(x) find f'(3) =

A: Given that: f(x)=4x2

Q: f (5), where f (x) = 1/(2x).

A: Given fx=12x we have to find f(5)

Q: Find f. f"(x)  =x6 - 4x4 +x +1

A: ∫xndx = xn+1n+1+C

Q: Find the general form of f if f'(x)= -7f(x).

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Q: If f(x) = 7+ 3 – 3x², find f'( – 5). -

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Q: 7- Differentiate Y= f(g(x4)) h³(√x)

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Q: – 5x+ 8x4 + 7x3 If f(x) find f'(x) %3D x4

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Q: If f(x)=x'2-2x+7 evaluate f(-5)

A: To find f(-5).

Q: Find (f-1)'(9) if f(x)=x3+x-1

A: To detemine the value of the derivative of the inverse function at the given point

Q: Find f. f"(x)  =20x 3    +12 x2    + 4  ,    f(0) =8,  f(1)  =5

A: Given, f''x=20x3+12x2+4f0=8, f1=5

Q: If f(x) – 5 + 3x 5a, find f'(3).

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Q: Find (f-1)'(3) if f(x) = x' + x+1

A: First find derivative then swipe the input and output for inverse of derivatives,

Q: Let f(x) = (9x² – 8)"(-8x² + 2)13 f'(x) =

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Q: If f(x) = (4x – 2)² - (3x² + 6)", find f'(4).

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