Problem 1 Solve the first order ODE with an initial condition y(1) = 2. Here yy(t) is the unknown and "" denotes the derivative with respect to t.

Q: Let f'(a) denote the derivative of the function y = f (x), calculated at x a. Prove that the…

A: Given,                  y= f(x)                      (1)

Q: Right- and left-hand derivatives Let f (x) = |x|. (a) Calculate the right-hand derivatives of f(x)…

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Q: 3. Find the derivative. sh (a)l= - पक) (a) f(x) = x2 cos x +x tan r (b) h(x) = e" (x² + 4x) %3D t2…

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Q: Find the derivative ( of the following functions dx a.y = (4x² - 1)(7x³ + x) b.y = e²x cos x sin x…

A: As per Bartleby answering guidelines if multiple sub part question are posted in single pic then the…

Q: 2. Find the derivative of the following functions: (a). f(x) = x* + 2x¯² + 4e* %3D (b). f(x) = 2 tan…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: * Problem 1: find the derivative j(x) = x24 + e²-4 + e²

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Q: -1 4.. у %3D 2а3 sinh "(6ӕ — 5) 2х-3 coth (x + 2) -1 5. у - 3 6x

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Q: х3 — 7 4.) у %3 7 - х' ,3 X y' =

A: Given function, y=x3-77-x3

Q: Let Q (p) : %3D p+1 (a) Calculate the derivative Q' (p) (b) Calculate the quotient Q (p + 4) – Q (p)…

A: Using derivative formula.

Q: 5. Find the derivative of y= x' +2x -1

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Q: Find the derivative of (a) f(z) = (z+4 sin z) (1-7 cos z), and %3D sin z (b) g(z)

A: Part (a) Given function is fx=x+4sinx1-7cosx

Q: Verify that each of the following difference approximations for the first derivative provides the…

A: As each approximation has independent of previous one . So according to guideline , I am verifying…

Q: 17) Find the derivative of y = x? COs x - 2

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Q: Find the derivative of h(x) = e³ + Vx + lnx. I

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Q: (а + 1)(а + 2) y = (а — 1) (а — 2)

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Q: 4. Find the following derivatives. (1) Suppose that y=sin(xcos x), find y (2) Find the first and…

A: Find the derivatives