Derivatives - Power, Product, Quotient Rules

Calculate the derivative using the product rule

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Calculate the derivative.

• f'(x)=x²cos(x)+2xsin(x)

• f'(x)=x²sin(x)+2xcos(x)

• f'(x)=x²sin(x)+2xsin(x)

Calculate the derivative.

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Which of the following is not a correct notation for derivative?'

• f'(x)

• y'

• dy

• dy/dx

Given y = sinx⋅cosx, y ' =

• -cosx⋅sinx
• sinx

• -sin²x + cos²x
• sin²x − cos²x

Let y = (x - 1)(x + 2). Find dy/dx.

• 2x + 1

• 2x - 1

• 4x - 1

• 2x² + x - 1

Find dy/dx for y = 4x³ + 3x + 1

• dy/dx = 4x² + 3

• dy/dx = 4x² + 3x

• dy/dx = 12x² + 3x

• dy/dx = 12x² + 3

• 8x⁴ -60x²
• 16x⁴
• (8x⁴ -60x²)/(2x²-5)²
• 3x

Find the derivative.
y = x² / (3x-1)

• y' = 9x² - 12
  y' = (3x-1) / (3x-1)²
• y' = (3x² - 2x) / (3x-1)²
• y' = (6x+1)² / 3

find 

• y = 2 x^-1
• y=2 x^-2
• y= −2x^-2
• y= −2 x^-1