Derivative Review

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

•  $-2x^2-x+9$  
  

•  $-2x^3-x^2+9x$  
  

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

•  $-2x^4-x^3+9x^2$  
  

Find the second derivative of the function $f\left(x\right)=2x-5x^6$  

•  $2-30x^5$  

•  $x^2-\frac{5}{7}x^7$  
  

•  $-30x^5$  

•  $-150x^4$  
  

 $\frac{d}{dx}\left[\sin\left(x^3-2x\right)\right]=$  

•  $\left(3x^2-2\right)\cos\left(x^3-2x\right)$  
  

•  $-\left(3x^2-2\right)\cos\left(x^3-2x\right)$  

•  $\cos\left(3x^2-2\right)$  

•  $\sin\left(3x^2-2\right)$  

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

•  $\frac{1}{\cos\left(5x^2\right)}$  
  

•  $-\frac{\left(10x\ \sin\left(5x^2\right)\right)}{\ \cos\left(5x^2\right)}$  
  

•  $-\frac{1}{10x\sin\left(5x^2\right)}$  
  

•  $\frac{-\sin\left(5x^2\right)}{\cos\left(5x_{ }^2\right)}$  

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 dy/dx by Implicit Differentiation
2/y = x²

• -4/x³
• x³
• 1/x²
• 2/x²

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

Tags

CCSS.HSF.IF.B.6

Which if the following is not a correct notation for 'derivative?'

• f'(x)
• y'
• dy
• dy/dx

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

The radius of a circle is increasing at a constant rate of 0.2 meters per second.  What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?

• 0.04π m²/sec
• 0.4π m²/sec
• 4π m²/sec
• 20π m²/sec

Tags

CCSS.HSA.SSE.A.1