The given function  y = 9x3e−x  is of the form  y = uv,  where  u = 9x3  and  v =  e−x       . Use the Product Rule,   d dx(uv) = u dv dx + v du dx, to differentiate y with respect to x. y '  =  d dx  9x3e−x     y '  =  9x3  −e−x   +  x         e−x     y '  =  9x2e−x    0

Q: Differentiate the function y = In (3x² – 6x + 7). Choose the correct setup below to start differe d…

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Q: 4) y = e3r* dy A) 12x dx B) dy 3* . 12x³ = e dx dy 3x e C) dx D) dy „3x* - 1 . 12x = e dx

A: Given below the detailed solution

Q: Use the product rule to help you find dy/dx for each of the following functions: 13. y = (x²)(2x -…

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Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: Differentiate the following functions: 6. y = csc-(2sinx)

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Q: 경기 Use implicit differentiation to find and 4x2 + 3y2 = 9 dx d²y 2 dx

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Q: Integrate 1. S the following: (x²-3x²) dx (x4-4x3+2)3 3 √x-2 z² 2 2. S dx 3. S dz 4 √73-2 3.

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Q: determine dy/dx of the implicit function: 2x2y-sinxy2+e-xy=10

A: Given implicit function is  2x2y-sinxy2+e-xy=10 To find: dydx

Q: Use implicit differentiation to find x³ + 3x?y + y° = 8 * + 3xy O A. * +y * + 2xy x² +y? OB. * + 2xy…

A: To find the derivative.

Q: Q4) Find for the following functions (- dx Зх +4 %3D 2x+3 6. y = tan-1 V4x3 - 3 %3D

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