Calculus Standard 7 - 9 Checkpoint

Find the derivative.
 f(z) = 1/(3z²) + 4z³

• f'(z) = 6z³ + 12z²
• f'(z) = 6z + 12x²
• f'(z) =  -2/(3z³) + 12z²
• f'(z) = -6/z² + 12z²

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

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

• A
• B
• C
• D

• A
• B
• C
• D

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

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

• y = 2x + 1 - 3x^-1

• y' = 4x + 1 - 1x^-2

• y' = 2 + 3x^-2

• y' = 4x + 1 - 3x^-2

Which of the following id the derivative for the following function?

g(x)= (x)/(4x³)

• g^'(x)= ((4x^3)(1) + (x)(12x²))/ (4x³)²

• g^'(x)= ((4x^3)(1) - (x)(12x²))/ (4x³)²

• g^'(x)= ((4x^3)(1) - (x)(12x²))/ (4x³)

• g^'(x)= ((4x^3)(1) - (x)(12x²))/ (12x²)

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

• y+1=2(x+1)

• y=2x-1

• y=2x+2

• y= -x-1