Differentiation Rules

When we find a derivative, we are finding... (Check all that apply)

• the slope of the tangent line

• the slope of the normal line

• the instantaneous rate of change of the function

• a bunch of algebraic gobbedy goo!

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

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

• 4
• x
• -4
• 0

Find the derivative of the given equation
f(x) = 1 - x²

• 1 - 2x
• -2x
• -2
• -1

Tags

CCSS.HSF.IF.A.2

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

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

Tags

CCSS.HSA.APR.A.1

What is the derivative of xⁿ?

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

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

• y = 500x + 400
• y = 100x + 400
• y = -500 x - 400
• y = 500x - 400

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Find the derivative of
 $f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$  

•  $-2x^2-x+9$  
  

•  $-2x^3-x^2+9x$  
  

•  $-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$  
  

•  $-2x^4-x^3+9x^2$  
  

Which of the following is the derivative of  $y=\left(3x^4-7\right)\left(5x^2+1\right)$  

•  $\left(12x^3\right)\left(10x\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$  
  

•  $\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$  
  

Tags

CCSS.HSA.APR.A.1