Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

Q: If F(x) = f(g(x)), where f( – 4) = 9, f'(– 4) = 6, ƒ' (2) = 1, g(2) = – 4, and g'(2) = 8, find…

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Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

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Q: Verify that g'(x) 1 where g(x) = v2x – 3. %3D V2r – 3

A: Giveng(x)=2x-3.To verify g'(x)=12x-3  is the derivative of g(x).

Q: Let 3 4 f(x) = (x° + 5x + 8)* f'(x) = f'(3) =

A: Chain Rule

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < ¤ < 1 and fx (5) = 5 then E (Y|X = }) =

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Q: Find F′(x).

A: Given Data The integral function is F(x)=ꭍxx+2(4t+1)dt.   Solve the given integral function,

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: Find y as a function of tif y(0) = 2, y'(0) = 3. y(t) = 0 16y" + 104y' + 169y = 0,

A:

Q: know that a3 .8

A: Antiderivative: F(x)=f(x9) F'(x)=f'(x9)*ddx(x9)       =f'(x9)*9x8 F'(a)=9f'(a9)a8       =9*13*6…

Q: If f(2) = 1, f'(2) = 2, g(2) = 2 and g' (2) = 1, then f(x) g(z) %3D %3D %3D

A: Given : f2=1f'2=2g2=2g'2=1

Q: If z = f(x) + yg(x), what can you say about zy? Explain!

A: Answer is 0

Q: Let r(æ) = f(g(h(x))), where h(1) = 3, g(3) = 2, h'(1) = 9, g/ (3) = –2, and f'(2) = 5. Find " (1).…

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Q: Let c =3 If f (x) : Cind f! (0

A: The function given is fx=x2-cx+1 The value of c given is 3. Substitute the value of c in the given…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(9) = 13, f(13) = 3, f'(13) = 12, f'(9)…

A: Given: Let F(x)=f(f(x)) and G(x)=(F(x))2 And f(9)=13, f(13)=3, f'(13)=12, f'(9)=10

Q: If ƒ(x) then f"(x) = · = 0 X (t³ + 5t² + 1) dt -

A:

Q: A. If G(2) = F(z) · H(z), then G' (3): %3D B. If G(w) = F(w)/H(w), then G' (3)

A: Given F(3)=1, F'(3)=2, H(3)=4, H'(3)=1.

Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(6) = 15, f(15) = 2, f'(15) = 7, f'(6) =…

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Q: Find y as a function of a if y"" - 12y" + 35y' = 24e", y(0) = 27, y'(0) = 11, y'(0) = 30. y(x) =

A:

Q: Let f(Vx)= 2x. Then f'(2) = -6 -4 6 4 8.

A: We need to substitution method

Q: Find the extreme values ​​of f(x, y) = 2xy subject to the condition x + y = 2.

A:

Q: Find y as a function of a if 2'y" + 6zy/ - 36y = 0, %3D y(1) = 1, y(1) = 5. %3D y =

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

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

Q: Prove this equation by deriving F(x, t) =X(x) Y(y). Please show full steps OF OF 2. +2x- =D0 Ditebak…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(5) = 11, f(11) = 3, f'(11) = 6, f'(5) =…

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Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

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Q: Let r(x) = f(g(h(x))), where h(1) = 2, g(2) = 3, h'(1) = 4, g'(2) = 3, and f'(3) 7. Find r'(1) %3D…

A: Recall: The derivative of a composition is the product of the derivative of the outer function (…

Q: Find f'(1) for f(x) = In(v6x – 3).

A:

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: f(z) = cos(4r +5) %3D

A: we have to derivative  we know that  d(cos (ax+b) ) = -sin (ax+b) a                        = - a sin…

Q: Let f(x) = 3x − 1, g(x) = x^2 + 1 and h(x) =x+1/3 Evaluate (h°f°g)(3).

A: f(x) = 3x − 1, g(x)=x2+1 and h(x) =x+13 To Evaluate (h°f°g)(3).

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

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Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

A: