v(x)u'(x) then h(x) = u(x))~ u(x) + (In (u(x))v'(x)) thenh(x)= u(x)" Use the above definition to find the derivative of the following function. 3x h(x) = (x² + 4) ³x If h(x) = u(x)(x), d -h(x) = dx

Q: Calculate the derivative of the function. (z^ + 6+x^) - (주) (F) P'(x) = +(x+9)(2) (F)* +1 (++9)(4)*…

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Q: 1. Using Definition of Derivative to find f'(x): a) f(x) = 2x² b) f(x) = x³ c) f(x)=√x+1 d) f(x) ==…

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Q: Let f(1) = 6, f'(1) = 7, g(1) = 4, g'(1) = 5, f(6) = 2, and f'(6) = 5. Calculate the following…

A: Use the chain rule of derivative and put x=1 than simplify using only those values which requires.

Q: T(x) T'(x) Find (A) the derivative of without using the quotient rule, and (B) B(x) . Note that the…

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Q: Q1: (a) Let f(x) = e-2". Find the first three derivatives of f(x): f'(x), f"(x) and f"(x). (b) Find…

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Q: Consider the function. f(x) = x R(x) + Q(x) Identify the derivative f'(x). f'(x) = xR'(x) + R(x) +…

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Q: Assume that the first derivative of a function y = f(x) is given by (x² + 1) (x² – 4)² ' Thus, which…

A: According to question that :y'=-x2+1x2-42

Q: In(x²) What is the derivative of

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Q: If f(x) = and g(x) = Vx, then the derivative of f(g(x)) is -VE (A) ( + 1) (B) -(x + 1)- -2x (C) ( +…

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Q: let f(x) be a function such that its derivative is given by: f'(x)=5(x-1)^2(x-2)^3(x-3)^4. which…

A: Consider the graph of given first derivative: If the graph of f '(x) changes from negative to…

Q: 2x+1 -2 x3 - 5x Which of the following is the derivative of f(x)= (x3 -5x)(2)- (2x+1)(3x² - 5) (x² -…

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Q: an anti derivative of 15 F(X) = (x²) F(x) = (x²) Explain why or why not

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Q: Find the anti-derivative of g(x) = 3x² which contains the point (-1,0). G(x) = 3x² - 1 O G(x) = x³ +…

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Q: Find the derivative of the function g(x) = (2a? – x + 5)e"

A: Our Aim is to find the derivative of (2x2-x+5)ex.

Q: Consider the following functions. f(u) = u + 1 h(u) = yu+1 p(u) = 1 − 5u² q(u) = (1 - 5u2)6 g(u) =…

A: If you have any problem let me know in comment box thank you.

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: Assuming all indicated derivatives exist. d ff{x) g(x)] is equal to : dx h(x) ƒ f'(x) g '(x) h(x) –…

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Q: Let g(x) 10x + 12 3x + 6 Find the derivative of g'(x). g'(x) =

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Q: Let F(x) = sin(x) ex a) Find f'(x), F"(x), f (³) (x), F"" (x) b) Find f (2) (x), the 2n-th…

A: Here, we have to find the derivatives of f(x)=sin(x)exWe shall be using the product rule of…

Q: What is the derivative of In(x?) et2 2e*? – 2x?in(x²)e*² (A) et2 2e*? – 2x?in(x²)e*² B xet? 2–…

A: We have to solve

Q: Let f(x): = x + 6 x + 5 (a) Compute the difference quotient of fly)

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