Let Y(s) = {y(t)}. Then L{ty"(t)} equals (i) sY (s)- y(0) (ii) s²Y(s) - sy(0) — y' (0) (iii) sY'(s) - sy' (0) (iv) y(0) s'Y'(s) — 2sY (s) (v) None of them

Q: A table of values for f, g, f', and g'is given. f(x) g(x) 3 2 x 1 2 3 ليا 1 7 8 2 (a) If h(x) =…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Let H(x) = F(G(x)) and J(x) = F(x)/G(x). Suppose F(4) = 9, F'(4) = -7 G(4) = 3, G'(4) = 0 G(-6) = 4,…

A: Given H(x)=F(G(x))H'(x)=G'(x)*F'(G(x))J(x)=F(x)G(x)J'(x)=G(x)F'(x)-F(x)G'(x)G2(x)

Q: Let f(x) = x7 Then f'(x) is 5æ5 + 3x³ – 3æ – 4. За — - - f'(3) is f' '(x) is and f''(3) is

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Q: If f(x) = (x² +2) e², what is f'(x)?

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Q: Let g(s) = (5s – 8)*. - Then g'(s) is g'(3) is s! (s),,6 and g''(3) is

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Q: (x"^y2/5)20 1/4 2/5 (x' (2) 2

A: since you have asked multiple questions in single request so we will be answering only first…

Q: 5. If y=5x²-3x + 10, give y'(-1)

A: We have to find the y'(-1).

Q: The derivative of h(y) = (2y² − 3y)˚(y + 6)² requires the product rule and is given by h'(y) = (2y²…

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Q: 6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the…

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Q: f(x) = In (x² + 1) %3D Note: 2x and f"(x) = 2(1 – x)(1+ x) (x² + 1)² f'(x) %3D %3D x2 + 1 (a) Find…

A: Here, we are going to solve the first two subparts and for the remaining subpart please post the…

Q: d²y If y= 2 f(g(x)), then dr²

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Q: f (x) You are given h(x) = f(g(x)); p(x) = f(x)·g(x); q(x) = g(x) and the following values f(2) = 1,…

A: Given : hx = fgxpx = fx·gxqx = fxgx

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: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: If we let f(x) = 1-4x/1+4x What are.... f’(5) = f”(5) = f”’(5) =

A: we have to find derivative at that point

Q: 1 (a) y= %3D - (b) f(x) = 3(r³ – e²) %3D 4 (c) h(x) = 3x³. %3D

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Q: y" – 12y" + 32y = 42e",

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Q: f(3) = 5, g(3) = -4, f'(3) = -2, g'(3) = 7, f'(5) = 3, g'(5) = 10 a) If h(x) = f(x)g(x), find h'(3).…

A: topic - functions and derivatives

Q: If f(x) = 5x4 – 2x3 –x² + 3x – 1, then | f'(0) = d2 ;f(0) = dx f"'(x)= d4 ¡f(x)= dx

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Q: If f(x) = (2² + 5x + 3)“, then s'(#) - [ f'(x) -

A: To find the derivative of the given function, we need to use chain rule of differentiation and some…

Q: If f(4) = 3 and f'(x) 2 3 for 4 s xs 9, how small can f(9) possibly be? (9) 2

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Q: If y = (3x+8)x, compute y'(1). y'(1) = X

A: We know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x The Product rule:…

Q: 2 If f(x) = (x³ +3x)“, what is f'(æ)? O f'(x) = (x³ + 3x) O f (x) = (x³ + 3æ) (3a² + 3) O f'(x) = 2…

A: Follow the steps.

Q: If g(t) = 1t¹ — 9t² – 3 find g(0) gʻ(0) = g''(0) = g'''(0) g (4) (0) g (5) (0) = = =

A: g(t)= t4-9t2-3

Q: f(x) = x* – }x' – x + 2x –1 -

A: Given   f(x)= 14x4-23x3-12x2+2x-1has turning point at where the f'(x)=0differntiate f(x) with…

Q: Suppose F(4) = 6, F(6) = − 4, and F'(x) = f(x). 6 L² (2x²4 + 4 (x² + 4ƒ(x) + 10) dx

A: