Product/Quotient Rule, power rule

Multiple Choice

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• slope of the secant line

Multiple Choice

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

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

Multiple Choice

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

Multiple Choice

Which one is the product rule?

• f(x)g(x)
• f'(x)g(x)-f(x)g'(x)
• f'(x)g(x)+f(x)g'(x)
• f'(x)g'(x)+f'(x)g'(x)

Multiple Choice

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Multiple Choice

• 12x⁴ +3x²

• 20x⁴ +3x² +16x

• 3x⁵ +32x³ +6x² +8x

• 24x³

Multiple Choice

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

Multiple Choice

Given f(x) = ax² + 2bx. What are a and b if f'(x) = 8x + 6?

• a = 2 and b = 3

• a = 3 and b = 2

• a = 3 and b = 4

• a = 4 and b = 3

Multiple Choice

Find the y'

• y' = 2 x^-1

• y'=2 x^-2

• y'= −2x^-2

• y'= −2 x^-1

Multiple Choice

What is the derivative of sin(x)?

• -sin(x)
• -cos(x)
• cos(x)
• sin(x)

Multiple Choice

What is the derivative of cos(x)?

• sin(x)
• -sin(x)
• cos(x)
• -cos(x)

Multiple Choice

Given that y = (x+2)/(x-3), find y'.

• y' = -1/(x-3)²
• y' = -5/(x-3)²
• y' = (2x-5)/(x-3)²
• y' = (2x-1)/(x-3)²

Multiple Choice

Which option shows the same expression?

Multiple Choice

Which option is using correctly the quotient rule?

Multiple Choice

Differentiate 6x^⅔.

• 4x^-⅓
• 4x^-⅔
• 6x^⅓
• 4x^⅓

Multiple Choice

Differentiate y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

Multiple Choice

The derivative of 

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

Multiple Choice

Find the derivative of the given equation
f(x) = -4x

• 4
• x
• -4
• 0

Multiple Choice

Find f '(2)  if
f(x) = x² + 2x

• 2x + 2
• 6
• 12
• 2x