Derivatives of a Function

Derivatives of a Function

Multiple Choice

What is the derivative of a constant, C?

• C
• 1
• 0

Multiple Choice

Find the derivative of the given equation

f(x) = 7

• 7

• 0

• 7x

• 14

Multiple Choice

What is the derivative of xⁿ?

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

Multiple Choice

Find the derivative of the given equation
f(x) = x⁴ 

• x³ 
• 4x
• 4x³
• x⁴

Multiple Choice

Find the derivative of y=3x²

• 3x

• 5x

• 6x

• x²

Multiple Choice

Find the derivative of y=2x⁵

• 10x⁴

• 10x

• 7x⁴

• 7x

Multiple Choice

Find the derivative of y= -3x⁴

• 12x³

• 7x³

• -12x³

• -7x³

Multiple Choice

What is the derivative of $$f\left(x\right)=2\ \sqrt[]{x}$$

• $$\sqrt[]{x}$$

• $$\frac{1}{\sqrt[]{x}}$$

• $$\frac{2}{\sqrt[]{x}}$$

• D $$-\ \sqrt[]{x}$$

Multiple Choice

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x

Multiple Choice

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

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

Multiple Choice

What is the derivative of f(x) = 2x³ - 4x + 5?

• f'(x) = 6x² - 4x

• f'(x) = 2/3x² - 4x

• f'(x) = 3x² - 4

• f'(x) = 6x² - 4

Multiple Choice

Which function has the derivative of g'(x) = 4x³ + 2x - 1

• g(x) = 2x⁴ + 2x² - 1

• g(x) = x⁴ + x² - x

• g(x) = 2x³ + x³ - 2x

• g(x) = x⁵ + x² - x

Multiple Choice

Find the derivative.
f(x) = -8x^-3 + 5x - e^x

• f'(x) = -24x^-4 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x
• f'(x) = 24x^-2 + 5 - e^x
• f'(x) = 24x^-4 + 5 - e^x-1

Multiple Choice

Let y = (x - 1)(x + 2). Find dy/dx.

• 2x + 1

• 2x - 1

• 4x - 1

• 2x² + x - 1

Multiple Choice

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

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

Multiple Choice

• 4x²+8x+1
• 20x⁶+5x⁴
• 28x⁶+5x⁴-16x

Multiple Choice

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

Multiple Choice

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)

Multiple Choice

• x⁵ + 5x⁴ + 2x³ + 6x² + 5
• 28x⁶ + 45x⁴ + 6x² + 40x
• 4x² + 8x + 1
• 4x⁷ + 49x⁵ + 50x³ + 20x² + 5

Multiple Choice

• -36x⁸ - 80x⁴
• -4x⁹ - 80x⁷ - 16x⁵
• -4x⁵ - 20x⁴
• -16x⁸

Multiple Choice

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

Multiple Choice

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

Multiple Choice

• f '(x) =-8x⁵ + 12x³ + 8x/3x⁸ + 6x⁴ + 3
• f '(x) = 48x⁵ - 36x³
• f '(x) =-24x⁵ + 36x³ + 24x/16x⁴ - 24x² + 9
• f '(x) =-12x³ + 8x/9x⁸ + 18x⁴ + 9

Multiple Choice

• f '(x) = -5x³/x⁸ + 2x⁴ + 1
• f '(x) = -80x³
• f '(x) = -x³/x⁸ + 2x⁴ + 1
• f '(x) = -16x³/5

Multiple Choice

• f '(x) =-16x⁸ - 80x³/16x¹⁰ - 40x⁵ + 25
• f '(x) = 80x⁸
• f '(x) =-x⁵ - 5/x⁵
• f '(x) = -16x⁸ - 80x³

Multiple Choice

• f '(x) =6x⁷ - 30x⁴ + 30x³ + 30/4x⁹ + 20x⁶ + 25x³
• f '(x) = 6x⁸ - 30x⁵ + 30x⁴ + 30x
• f '(x) = 24x⁸ + 60x⁵
• f '(x) =2x⁸ - 10x⁵ + 10x⁴ + 10x/3x⁸ + 6x⁴ + 3

Multiple Choice

• f '(x) = 30x⁶ + 24x⁵ + 30x³
• f '(x) =25x⁴ + 16x³ + 4x/9x⁴ + 12x² + 4
• f '(x) =45x⁶ + 24x⁵ + 50x⁴ + 32x³ + 20x/9x⁴ + 12x² + 4
• f '(x) =45x⁵ + 24x⁴ + 50x³ + 32x² + 20/25x⁹ + 40x⁸ + 16x⁷ + 50x⁶ + 40x⁵ + 25x³