Find and d²y then simplify whenever possible. dx dx² 1) у %3D 3t5 — 2t x = 4t3 2) y = t-3 – 7 x = t² – 2t 3) y = 2u* + 1 ,x = 5 u? – 5u 4) y = /2t – 5 x = t² – 3 5) y = 2t3 – 3t , x = 4t² + 4t + 1

Q: find the derivative of x2-36.

A:

Q: What function could have −4x+20 as its derivative?

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Q: 2x + 1 2 arccot V3 || V3

A: The given function is:y=23arccot2x+13

Q: Solve for the second-order derivative of: [(4x3-1)(8x2+6x-3)]3

A: We have to calculate second order derivative of [(4x3-1) (8x2+6x-3)]3   Let us say  Y= [(4x3-1)…

Q: Determine if the following piecewise defined function is differentiable at x = 0. 4х- 1, X20 f(x) =…

A: We will check whether the function is differntiable or not at x=0 as following.

Q: 3x² (9 – x² ) 2 2 (9 — 3х2)

A:

Q: (c) y = e-a sin(ax + 3). (e) y = tan(5x) 52+1 (d) y = a √a² + x²

A: (d/dx)(af(x)) = a(d/dx)(f(x)) , where a is constant. (u.v)' = u.v'+u'.v (u/v)' = (v.u' - u.v')/v2

Q: Find the inverse of y= -9 -x1/3

A: We find inverse function of y = f(x) by interchanging x and y first and then solving new equation…

Q: Find the fifth derivative of (2x+3)5

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Q: F'irond, Che derivative: y

A: Given: y=6x+7x2-x+3 We know that ddxuv=vdudx-udvdxv2…

Q: Find dx * and then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t? –…

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Q: Acrsin a2_v2

A:

Q: Find the derivative of 22x - 10

A: Given:            22x-10 Solve: ddx22x-10 Apply sum/difference rule: ddxfx±gx=ddxfx ±ddxgx…