Find the solution of the following initial value problem 1 (4 x' = 2 1 X where x(t) = (21(t)) and x(0) = (-²)

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

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Q: (1) If f(x) = x¹0, then f'(x) =

A: According to bartleby guide line we do only first part of multiple questions. please re-post other…

Q: If h(x) = f (g(x)), where f(0) = 7, g(0) = - 1, f'(0) = 0, g'(0) = - 3, f(- 1) = - 3, g(- 1) = 2,…

A: We have hx=fgx

Q: If f(x)=4x2-2x+3 solve f'(x)=28

A: We first find f'(x) using exponent rule: [d/dx(x^n)= n*x^(n-1)]

Q: 17) y = x'e - x'e-2x

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Q: Find the equation of the tangent link to f(x)=x³+x²+x @x=3 A y=34x-63 B D y=-12x-36 y=12x-36…

A: 20) The function is  f(x)=x³+x²+x  Note:- As per the rules, we are supposed to answer the first…

Q: e) None of the above. 0 1 0 0 0 1 x is: he general solution of x' = -4 4 1 (1\ ( 1\

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Q: Find a particular solution to the following first by undertermined coficients,and then by variation…

A: Step 1: To find a particular solution to the given differential equation using the method of…

Q: If h(2) = 4 and h'(2) = π, find g'(2) where g(x) = 2x h(x) + cos(x)

A: To find out the derivative of the given function.

Q: If 4 – x2 f(x): 2 + x2 find f' (x). f' (x) =

A: Given function is Differentiating both sides with respect to x by using quotient rule of…

Q: Suppose F(3) = 2, F(8)= -19, and F"(x) = f(x). —13, and G'(x) = g(x). Also suppose G(3) =0, G(8) = =…

A: use integration  for finding the values.

Q: Solve the following questions: 1. If f(x)=17x+3, find f'(-3) 2. If f(x)= 13, find f'(-6) 3. If…

A: We are authorized to answer to answer one question at a time, so we are answering the three…

Q: GivenF(x) = h(f(g(x))), g(1) = 2, g′(1) = 3, f(2) = 4, h'(4) = 1 and f'(2) = 6, findF′(1)

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Q: 1. If f(x) = 5x4 - 6x² + 4x - 2 find f'(x) and f'(2).

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Q: If h(x) =/4+3f(x), where f(1) = 7, and f'(1) = 4, find the value of h'(1).

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Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f '(1). f '(1) =

A: Given:  f(x) + x2 [f(x)]3 = 10 and f(1) = 2

Q: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: lf ƒ(3) = 5, ƒ'(3) = 2, g(3) = 4, g′(3) = −2. Let h(x) = √g(x) f(x)-2g(x)* Find h' (3). 76 O-1 C 13…

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Q: 6. If f(x)=3x' -+ 4 + 4x +1, find f(x) and f"(x).

A: Given query is to find the Indicated derivative.

Q: 3x-5 12x+41 7. The derivative of g(x) = 8. The derivative of y = V5x² – 6 is y' = is g'(x) = (4x+7)2…

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Q: If fx)=5x-1, g(x)=1/x, and h(x)=g(fx)), then what is h'(0)?

A: Given that h(x)=g(f(x)) Using chain rule we get: h'(x)=g'(f(x))f'(x) We plug x=0 So,…

Q: 1) If h(a) = a + 1, find h-(x). (A) h-(x) = 3+ (x+ 2)3 (B) h-(x) = V – I (C) h-(x) = 2a3 – 3 %3D %3D…

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Q: Suppose h(x)= x² – 2xf(x). Find h' (5) given that f(5) = 4, f' (5) = -8. h'(5) =

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Q: 18) Suppose P'(x) = 5ex - 6x³+ 4x and P(0) = -9. Find P(x).

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Q: 10 (1) If f(x) = x¹0, then f'(x) = (2) If g(x) = -8x², then g'(x) = 1 (3) If h(x) = −3 then h'(x) =

A: The objective of these questions is to find the derivative of the given functions. The derivative of…

Q: 1. If h(x) = (f(x))² – (g(x))² , f' (x) = -g(x) and g' (x) = f(x), then h'(x) = (a) 0 (b) –4f(x).…

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Q: If f(x)=5x-1, g(0)=2, g'(0)=4, and h(x)=f(g(x)), then what is h'(0)?

A: Solution:

Q: 1. f(x) = 6x + 15 find f'(x) Answer:

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Q: Find f'(x). f(x) = (x² + 1) * f"(x) = %3D

A: Find f''(x)

Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,

Q: Suppose H(x) = f(g(x)) and %3D f(14) = 3 f' (2) = 13 g(14) = 2 d (14) = 4 Find H' (14)

A: Chain rule of differentiation:

Q: If f(x) = x° + x³ + x, find f ¯'(3) and f(f¯'(2)). %3D

A:

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

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Q: If f(1) = 5 and f'(x) > 2 for 1< x < 6, then the smallest value of f(6) would be

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Q: Given ƒ(7) = 3 and f'(7) = 4 find the value of h' (7) based on the function below. h(x) = (f(x))²

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