Let y = 3x(In x)², find dy and d²y dx dx2" A. dy 6 В. dy 6x + 3(In x)²; dx + 3 In x; dx d²y dx2 6 In x 6х + d²y dx² 2 In x 6х + C. dy 6ln x + 3(ln x)²; D. dy = 6 In x + 2(ln x)3; dx dx d²y _6 6 ln x = -+ dx² d²y_63(ln x)² dx

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Q: 9-x2 x dx

A: ∫9-x2x2dx=∫cot2udu=∫ -1+csc2udu=-∫ 1du+∫csc2udu=-u-cotuSubstitute back…

Q: (A) If y = 5x x² - 4 dy dx dy dx dy dx dy then = dx −5x2 — 20 (x² - 4)² 5x2 – 20 (x²-4)² −5x2 +20…

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Q: -2 S₁² S₁² (²x²y^² + 2 (2x²y-² + 2y) dy dx 1 1

A: Given- ∫12∫1x(2x2y-2+2y)dydx To evaluate the given integral.' Here we will use the following…

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A: To find the derivative

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Q: 2ydx-(1-x^2)dy=(x^2-1)dx when x=0 and y=-1

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Q: If y=3(−7x^2+7x+1)^13, then      dy/dx=

A: Given:- y= 3(-7x2+7x+1)13 To find :- dy/dx

Q: *y=(2x^2+6) find dy\dx 4x\(2x^2+6) O 6x O 4x\(2x^2+7) O

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Q: Find * dy ,If y 3 dx + x O x^2 + x O x^3 + x^2 +1 O x^2 + x + 1 O 3x^2 + 2x + 1

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Q: (2x+1)dx (x+2)^(x–1)“ (x+6)dx S (æ+2)² dx S æ (1+a²)

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Q: Find d^2y / dx^2 when y = 8+x / 4-x

A: Simply take two times derivative of the given equation using the derivative of the form  u/v

Q: 11. x² +1 Find +3x+1 -dx

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Q: dy If y = ( a² +1) (x³ + 3) dx %3D O 5x^4 + 3x^2+ 6x 6x^3 O 2x + 3x^2 O 2x^2 +2x+ 3x^5+9x^2…

A: Question 1,Given,            y=x2+1x3+3To find: dydx

Q: 8. (x² + 2xy − 4y²) dx — (x² − 8xy — 4y²) dy = 0. - -

A: #8

Q: 4. x(x² – 1)² dx

A: Solution:

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Q: Suppose dy/dx= (3x+1) √(3x^2+2x) and y(0)=1. what is y(5)?

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A: Evaluating the integral