Find the first and second derivatives of the following. 1-4√√x+x³ (a) y = (b) y = 3x²e² Y (c) y = x³ sinx

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Q: 1. Verify y(x)=c, sin x + c₂ cos x −(cos x)In(secx+tan x) is a solution to y" + y = tanx.

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A: As we know that

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A: Given equation, .derivative rules:

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Q: 7x 1+2x 2+1 x_3+8 x_4+9x_5 = 69 9x 2+3 x 3+4x_4+4 x 5 = 54 4x 1 + 6 x 2+5 x_4+4 x 5 = 40 2x 1 + 10 x…

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Q: ind the following limits. -2x³ - 6 x→∞ −5x² - 7x - 8 a. lim -2x³ - 6 x→→∞ −5x² – 7x - 8 b. lim ||

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Q: Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

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Q: Find the local minimum of the function f(x), which is given in the graph below. -6 -5 -4 -3 -2 -1 6…

A: To find the local minimum of the function , which is given in the graph below.

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Q: Compute the differential dz of the function. = x ¹⁰y5

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