Basic Derivative Rules Practice

What is the derivative of    $y=\left(3x^{ }-7\right)\left(5x^2+1\right)?$  

•  $y'=30x$  
  

•  $y'=45x^2-70x+3$ 

•  $y'=-15x^2+70x+3$  

•  $y'=45x^2-67x-4$  

What is the derivative of a constant, C?

• C
• 1
• 0

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n-1)x^n-1
• nx^n-1

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Set up the derivative of

y=(3x⁴ - 7)(5x² + 1)

• y' = (12x³)(10x)

• y' = (3x⁴ - 7)(10x) + (12x³)(5x² + 1)

• y' = (3x⁴ - 7)(10x) - (12x³)(5x² + 1)

• y' = (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Use the quotient rule to determine the derivative.

• 8x⁴ -60x²

• 16x⁴/(2x²-5)²

• (8x⁴ -60x²)/(2x²-5)²

• 3x

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$  

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$  

• 4x²+8x+1
• 20x⁶+5x⁴
• 28x⁶+5x⁴-16x

• 5x⁴ + 20x³ - 2
• -160x⁷+140x⁶ - 48x³ - 24x²
• -80x⁷+ 60x⁶ + 32x³ - 24x²

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