Product and power rule Calculus

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.

• f'(x)= -5xsin(x)+cos(x)

• f'(x)= 5xsin(x)+5cos(x)

• f'(x)= -5xsin(x)+5cos(x)

Calculate the derivative.

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

• f'(x)
• y'
• dy
• dy/dx

Tags

CCSS.HSA.REI.A.1

Find the slope of f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Tags

CCSS.8.EE.B.5

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

Find the derivative of y=5x⁴

• (5x³)/4
• 20x⁴
• 20x³
• x⁵

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

The derivative of 

• y'=2x-x^-2
• y'=x^-1+8x
• y'=x^-2+8x
• y=8x-x^-2