Given x(t) = t^3 − 3t + 1 y(t) = t(t + 1)  Find the value of t at points (1,0) and (3,6)

Q: If ƒ(t) = (t² + 6t + 7) (7t² + 2), find f'(t). Find f'(2).

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Q: If f(t) = (t + 7t + 3) (5t² + 6), find ƒ'(t). Find f'(5).

A: Given : ft = t2 + 7t + 35t2 + 6

Q: 1+vx [8] Find y" of y =

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Q: Let f(x) = √6-x The slope of the tangent line to the graph of f(x) at the point (2, 2) is The…

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Q: Find y as a function of t if y(4) = 6, y (4) = 4. y = 121y" - 132y +36y = 0,

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Q: Solve For the orthogonal trajectories (a+x) y² = x² (3a-x)

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Q: If f(t) = (t + 7t + 3) (5t? + 4), find f'(t). %3D Find f'(1).

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Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: f(t) = (t + 4t + 8)(7t¯² + 6t).

A: Given function is: ft=t2+4t+87t-2+6t-3 Then we get,…

Q: Utt u(x, 0) ut (x, 0) = = = 4uxx x² + 3x

A: USIND D'ALEMBERT'S SOLUTION FOR ONE DIMENSIONAL HOMOGENOUS WAVE EQUATION ,WE HAVE

Q: If f(t) = (t + 5t + 4) (2t² + 2), find f'(t). Find f'(3).

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

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Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

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Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Q3 Find f-(x) for the following : 1- y = Jx-3 2- y = (2x³ + 1)'/5

A: For finding the inverse, we will replace x with y and y with x

Q: (x³-4x+1)vx++5x+5 find y' 4x2+5x

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Q: P(t)=12t 4 -6f +=+7 .3 y 3 (x³ +2x +7) (4–x²

A: Given: P(t)=12t4-6t+5t+7y=(x3+2x+7)(4-x2) We have to find the derivatives of the given expressions.…

Q: Find y as a function of a if y" - 3y" y + 3y = 0, y(0) = -7, y' (0) = -4, y" (0) = 9. y(x) =

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