Equations of Derivatives

Multiple Choice

Find the derivative of $$f\left(x\right)=x^4$$

• 
  $$f'\left(x\right)=4x^2$$

• $$f'\left(x\right)=4x^3$$

• $$f'\left(x\right)=x^3$$

• $$f\left(x\right)=5x^3$$

Multiple Choice

Find the derivative of $$h\left(u\right)=u^{-1}$$

• $$h'\left(u\right)=-1u^0$$

• $$h\left(u\right)=-u^{-2}$$

• $$h'\left(u\right)=-u^{-2}$$

• $$h'\left(u\right)=-u$$

Multiple Choice

Find the derivative of $$g\left(x\right)=7x^2$$

• 14x^2
• 14x
• 3x^2
• 7x

Multiple Choice

Find the derivative of $$y=6x$$

• 12
• 3x
• 0
• 6

Multiple Choice

Find the derivative of $$z=\frac{3}{x^2}$$

• $$z'=6x$$

• $$z'=-6x^{ }$$

•  $$z'=-6x^{-1}$$

• $$z'=\frac{3}{2x}$$

Multiple Choice

Find the derivative of $$f\left(x\right)=-\frac{5}{3x^3}$$

• $$f'\left(x\right)=5x^{-4}$$

• $$f'\left(x\right)=\frac{5}{3}x^{-3}$$

• $$f'\left(x\right)=15x^{-4}$$

• $$f'\left(x\right)=5x^4$$

Multiple Choice

Find the derivative of $$f\left(x\right)=x^2-4x$$

• f'(x) = 2x - 4
• f'(x) = 2x^2 - 4x
• f'(x) = x - 4
• f'(x) = 2x + 4

Multiple Choice

Find the derivative of $$f\left(x\right)=3x^3-5x^2+7x-2$$

• f'(x) = 6x^2 - 10x + 7
• f'(x) = 9x^2 - 10x + 7
• f'(x) = 3x^2 - 10x + 7
• f'(x) = 9x^2 - 5x + 2

Multiple Choice

Find the derivative of $$y=3-2x^3+\frac{1}{4}x^4$$

• y' = 3 - 6x^2 + x^4
• y' = 12x^3 - 2x
• y' = x^3 - 6x^2
• y' = -6x^3 + x^2

Multiple Choice

Find the derivative of $$f\left(x\right)=x^3\left(2x-5\right)$$

• 3x^2(2x-5)
• 6x^2 - 10
• 8x^3 - 15x^2
• x^3(6x-15)

Math Response

Find the derivative of $$h\left(x\right)=\left(1+\frac{1}{x}\right)^2$$

Type answer here

Correct Answer: -2x^{-3}-2x^{-2}

Deg^°

Rad

Multiple Choice

Differentiate the expression with respect to x: $$\frac{x+10}{x}$$

• $$-10x^{-2}$$

• $$10x^2$$

• $$10+\frac{1}{x}$$

• $$-x+10$$

Multiple Choice

Differentiate $$\frac{x^2+3x^3}{2x}$$

• $$\frac{x}{2}+3x$$

• $$-\frac{1}{2x^2}+3x$$

• $$\frac{x^{-1}}{2}+3x$$

• $$\frac{1}{2}x^{-2}+3x$$

Multiple Choice

Find the interval of values of x for which the function $$f\left(x\right)=3x^2-6x+2$$ is decreasing.

• (1, ∞)
• (-∞, 0)
• (0, 1)
• (-∞, 1)

Multiple Choice

Find the interval of values of x for which $$f\left(x\right)=-x^2+12x-9$$ is decreasing

• (6, ∞)
• (-∞, 6)
• (3, 6)
• (0, 6)