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: 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: dx Vx2-4 2.

A: Let's find integration.

Q: Determine using implicit differentiation. dy dx 4x³ +2y³ = 3y 2x³y² + 5y³ = 4x-1 2x 3x + y =y Note:…

A: 1st...4x3+2y5=3y2nd....2x3y2+5y3=4x-13rd....2x3x+y=y

Q: if y = 3x2-2x+5 , determine dy/dx using the definition.

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Q: S(3 – x) dx 12

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Q: 3. Sx² tan (3x-1) dx

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Q: Differentiate. In x y= 11 y3D dx

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Q: Find √√3 x² +3 x² +1 dx

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Q: 2х-у x3 x+3

A: The given function is x3=2x-yx+3y

Q: Differentiate the function. y = (3x- 1)* (4 - x5) 3 dy dx II

A: To differentiate the given function:

Q: bxe* dx хе (х+а)2

A: To evaluate the given integral

Q: Differentiate implicitly to find d2y/dx2.   3y2−xy+5x2=5

A: Differentiate implicitly to find d2y/dx2.  3y^2−xy+5x^2=5

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: Evaluate I = / a*. g³ Vx² – 3 dx

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Q: 1-√x)³ 3 √x dx

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Q: Evaluate dy/dx if y = (sec2x - tan2x)/(2cos2x-1)

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Q: x³ +4x² + x – 1 dx 2 X 16. .3 2 1 x' + x'

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

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Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

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