1 (1) u(x) = x + f * u(t)dt, u(x) = x+ 24 2 (2) u(x) = ² = x + √² xtu(t)dt, u(x) = x (3) u(x) = x + [xtu²(t)dt, u(x) = 2x

Q: If f(x) = f'(x) = 1 x³ 3 √t² + 1 dt then F

A: Here we will use the Leibniz theorem to  find the derivative of the given problem, so on using this…

Q: What is tl

A: Given function is: f(x) = 3 + cos (3x) We have to find the gradient of the function.

Q: From the previous page: the function f(x) = e*(x² + x – 1) has derivatives f'(x) = e*(x² + 3x),…

A: Consider the following function: fx=exx2+x-1f'x=exx2+3x Consider the part (e): Linear approximation…

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I…

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Q: - (7)f | dt, then f (z) 1.

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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: Show that P2(x) = f(a) + f'(a)(x − a) + c2(x − a)2 for each value of c2 satisfies the requirements…

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Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: If ƒ(x) = f (t³ + 5t² + 7) dt then ƒ"(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(2) 1 dt, then f'(z) = ++1

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Q: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

Q: (5) Find the domain of the function f(x,y) = ²-In(r+2) 2-y√100-2² - y²

A: Remember the following domain For xy, y≠0 For x, x≥0 For lnx, x>0 Given function…

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: a) If F(x) = | 1 dt, then F'(x) = t 14 1 b) If F(2) = dt, hen F'(2) = 1 c) If F(x) = / dt, then…

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Q: Let F (x) = (1 + t2)/5 dt - Then F'(x) =

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Q: 1. Find the second derivative of f(x) = x5 – 4x + 1. а. 5x3—4 ь. 20х3 с. -20х3— 4

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Q: (-y dx + xdy) = (a) d(xy) (b) d(y/x) (c) d{ In(xy) } (d) -d(x/y)

A: By quotient rule , duv = v du-u dvv2

Q: dt, then F'(x) = 0 a) If F(x) = √5 / / di 20 3 b) If F(x) = ² = dt, then F'(x) = c) If F(x) = √²/1/1…

A: Given:   a) Fx=∫20x1tdt      we use common integral ∫1tdt=lnt          =lnt20x          Fx=lnx-ln20…

Q: For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

A: The given matrix is, A=4635. The function is f(x)=x2-5. For matrix multiplication: The number of…

Q: Consumption C(t), investment I(t) and national income Y(t) at time t satisfy the equations: C(t) +…

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Q: Let f(x) = 1 + x³ + dt. Determine the value of (f-1)'(0).

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Q: Find c'(t) and ||c'(t) || - c'(t) = (2e',41,2) (2e*, 4t, 2) ||c'(t)|| = V 4e + 4t + 4| 2t 4²? - 4e2t…

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Q: Calculate the linear approximation for f(x): f(x) × f(a) + f'(a)(x - a). 3 at a = 1 f(x) = 2+x L(x)…

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