Derivative Rules Quiz

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

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

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line

What is the derivative of cos(x)?

• -cos(x)
• sin(x)
• cos(x)
• -sinx

What is the derivative of tan(x)?

• -sec²(x)
• -csc²(x)
• sec²(x)
• csc²(x)

Tags

CCSS.HSF.TF.C.9

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

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

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

•  $y'=30x$  
  

•  $y'=45x^2-70x+3$ 

•  $y'=-15x^2+70x+3$  

•  $y'=45x^2-67x-4$  

Tags

CCSS.HSA.APR.A.1

An equation of the line tangent to the graph of

 $g\left(x\right)=\frac{3}{x^2+2}$  when  $x=-1$ is

•  $y=\frac{-2}{3}\left(x+1\right)-1$  

•  $y=\frac{-2}{3}\left(x-1\right)+1$  

•  $y=\frac{2}{3}\left(x+1\right)+1$  

•  $y=\frac{2}{3}\left(x-1\right)+1$  
  

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If  $h\left(x\right)=f\left(x\right)+g\left(x\right)$  Find $h'\left(2\right)$  

•  $\frac{3}{2}$  

•  $\frac{-3}{2}$  

•  $\frac{-1}{2}$  

• 1

Tags

CCSS.HSA.SSE.A.1

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If  $h\left(x\right)=f\left(x\right).g\left(x\right)$  Find $h'\left(1\right)$  

•  $\frac{3}{2}$  

•  $2$  

•  $\frac{-1}{2}$  

•  $-3$