Consider the equation di(t) +7² [i(x) with the initial condition i(0) = 0. ["i(x) dr = e(t), t≥0,

Q: Let h(x) = f(x)g(æ). If f(x) -3x? – 4x + 2 and g(x) = -x² + 3x +2, what is h' (-1)? Do not include…

A: Given, h(x) = f(x)g(x) f(x) = -3x2 - 4x +2 g(x) = -x2 +3x +2  We have to find h'(-1)

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: 3) Consider the function G(x) = f g (t) dt. Find the derivative G' (x). O g(x) g(x)-g(1) O g(t) O…

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Q: Find the first and second order derivatives of the function (a) f(x) = 0.001x5 -0.002x³ (b) G(r) =…

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Q: If h(x)=√ 7 + 6f(x), where f(1)= 7 and f (1)= 2, find h(1). h'(1) = x

A: Given function Where

Q: x () - (-). y (1) J

A: Givenf(t)=sect   We are required to find f''π4

Q: Let g(x) = x³ – 2x + 6. Find f(x) so that f'(x) = g'(x) and f(1) = 2. NOTE: Enter the exact answer.…

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Q: ren that f(x) = 6x - 6 and g(x) = 2- r', calcula f(g(0)) %3D 9(/(0)) - %3D

A: The question is taken from the above function and we have to find the composite function at the…

Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: Find y as a function of a if y(0) = 19, y'(0) = 26, y" (0) = 14. y(x) = y"" - 10y" + 21y' = 48e²,

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Q: Given f(4) = 13, f '(4) = 19, g(4) = 7, and g'(4) = – 10, find the value of h'(4) based on the…

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Q: 6 - 7t g(t) 8t + 9 g'(t) =

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Q: Find y as a function of t if y(0) = 2, y'(0) = 5. y(t) = 100y" +9y = 0,

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Q: 2x 1) Calculate the derivative of h(x) = √√e²x +e-²x

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Q: or h' (x):

A: Given that: The equation is h ( x) = g ( x 2 + f ( 3x) ).

Q: 12.Find the derivative of f(x) = x²e2x-6 at x = 3. (A)–16 (B) -12 (С) —18 (D) 20 (E) 24

A: Given : f(x) =x2e2x-6

Q: Find y as a function of t if y(0) = 8, y'(0) = 4. y(t) = 6y" + 33y = 0,

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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