Find the Slope Using Derivative

• 12x⁴ +3x²
• 20x⁴ +3x² +16
• 3x⁵ +32x³ +6x² +8x
• 24x³

Which of the following are synonyms for find the derivative?

• f'(x)

• dy/dx

• y'

• slope of the tangent line

• instantaneous rate of change

Which option is using correctly the quotient rule?

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Let f(x) = (x - 1)(x + 2). Find f'(0)

• 0

• 1

• 2

• 3

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2

• 3(x²+2)/(x²+2)²

• (-3x²+4x +6)/(x²+2)²

• (-3x²+10)/(x²+2)²

Is differentiating the same as taking the derivative?

• yes

• no

• sometimes

Use the product rule to determine the derivative.

• 4x⁸+60x⁶+12x³

• 12x⁷+36x²

• 32x⁷+36x²

• 20x⁶

Find an equation of the line tangent to the curve f(x)=(x-2)(x+1) at the point (1,3)

• y=x-2

• y=x+2

• y=6x+1

• y=x