If a(x) is an integrating factor for y' + A(x)y = B(x), then a'(x) is equal to: Ο α(x)A(x) Ο α(x)Β(x) O a(x)A'(x) B(x)

Q: Let A(x) be the function defined by A(x) = 4 We have A(0) = -3 A'(-1/2) = -2 for x = [-1,0], A(x) =…

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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: X If f(x)=. 2/x+1 f'(x) is given by:

A: Given Data: Function: fx=x2x+1   The Quotient rule of differentiation is, ddxfxgx=gxf'x-fxg'xgx2…

Q: Let r(x) = f(g(h(x))), where h(1) = 3, g(3) = 6, h'(1) = 3, gʻ(3) = 3, and f '(6) = 5. Find r'(1).…

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Q: Let f(x) 11 In(x). Then f'(x) is andf (8) is f"(2) is and f(8) is

A: Use differentiation for finding the values

Q: If f(x) = [ sin(x) = ['(x) 6 3+ t² dt and g(y) = f(x) dx, find g (7). 6

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Q: 4. Let f(x) = e3h(x) and g(x) = h(e3"). Find f'(7) and g'(2) given that h(7) = 2, h'(7) = 4, h'(e) =…

A: We have to find

Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=

A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .

Q: If f( x ) = sin (x) – e“ , what is f'(x) ? O f'(x)=- cos(x)-e² — сos(2) —е* O f'(x)=sin (x) –e² O f…

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Q: f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = −1, g(1) = −2,…

A: Product rule:

Q: If f(x) = 1' + 3, g(z) = z – 3 and h(x) = VI, then f(g(h(x))) =

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Q: x²+2x=1 then f'(1) is Let f(x) = 2x3+1

A: we have given f(x). And we have to find f'(1)

Q: f'(x) = f'(4) - L

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Q: Do not use technology. Consider the following table. (a) If h(x) = h'(2) f(x) g(x) X 2 5 f(x) f'(x)…

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Q: et f (x), g (x), h (x) be differentiable functions. Suppose g(x) is invertible. iven that f (2) = -,…

A: Given query is to find the derivative if the expression.

Q: Let h(x) = In[(f(x))² +1. Suppose that f(1) = -1 and f' (1) = 1. Find h'(1).

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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: (b) If F(x) and G(T) are two different antiderivatives of the same function, then F'(x) #G'(x).

A: The given statement if F(x) and G(x) are two different antiderivatives of the same function then…

Q: g(x, y) = sin (T ¤y) + log3 (x – 3y) -

A: The given function is                          gx,y=sinπxy+log3x-3y…

Q: Let r(x) = f(g(h(x))), r'(1) = where h(1) 2, g(2) = 3, h'(1) = 4, g'(2) = 5, and f '(3) = 6. Find…

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Q: Let r(x) = f(g(h(x))), where h(1) = 4, g(4) = 6, h'(1) = 3, g'(4) = 5, and f '(6) = 8. Find r'(1).…

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Q: Given the focus and directrix of the graph of a parabola identify its vertex and focal width.

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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: what valu e shouled be assigneed to a to make the function fex)= %3D 2ax

A: For the function to be continuous, the necessary condition is LHL=RHL=f(3) Here,  LHL=limx→3-f(x)…

Q: If x f(x)+x g(X)= sin x, for nonzero x, then f''(X) + g''(x) is %3D

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Q: Let g(x) = = X-f(x) S(x) , find g'(1),if f(1) = 4 and f'(1) = 2

A: Given that g(x) = -x-f(x)f(x). We have to find the value of g'(1). Given that f(1) =4 and f'(1) =2.…