Theorem: Constant Multiple Property If y = f(x) = k· u(x), where k is a real number and u(x) is a function, then the derivative is Of'(x) = k + u'(x) ○ f'(x) = k-u' (x) ○ f'(x) = k· u(x)k-1 ○ f'(x) = 0

Q: Find the derivative

A: To calculate the derivative of f(x) at x =0

Q: ●y = (x+1)² √x+1 W= t+1 t-1 -t -)×(1-1 1-2t

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A: Given function, f(x)=x2+x2

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Q: the number lines for f(x), f'(x) and f''(x)

A: Given f(x)=e-x3x+1 To draw the number lines for  f(x), f'(x) and f''(x). and determine the concavity…

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A: The given function is

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Q: 1 th X +7 Fy =

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Q: Evaluate the derivative of y = (x 2+ 2x + 1)2usingd/dx (ƒ(g(x)) = ƒ′(g(x)) # g′(x)

A: We have to evaluate the derivative ofy = (x2+ 2x + 1)2usingddx(f(g(x))=f'(g(x))*g'(x)

Q: 20 – 33 Use the method of Laplace transforms to solve each IVP. 32. y""+ 4 y" - 5 y' = 0, y(0)% 3D4,…

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Q: Use the Product Rule or Quotient Rule to find the derivative of f(x) = O None of these. f'(x) =…

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Q: Find the derivative of f(#) v5-tan(r)

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Q: Given that f(3) = 2, f'(3) = 5, g(x) h(x) = f(x), then find g'(3), and h'(3) = f(x)

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Q: e picture below shows the graph y = f'(x) of the derivative of f(x). alues are labeled 'A', 'B',…

A: Since you have asked multiple part question, we will solve the first part of question for you as per…

Q: Can you please help me step by step with this problem?

A: The given function is f(x) = 2+x2.

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Q: 3x Let f (x) = Then the derivative of f is 1 + 5x f'(x) = A(1 + 5*) – Bx(5*) lIn C_ (1 + 5*)D where…

A: Given: f(x)=3x1+5x To find: A, B, C, and D if f'(x)=A(1+5x)-Bx(5x)ln C(1+5x)D              ...(i)