AP Calculus AB Derivatives

Find the slope of  $y=3x^2-5$  at the point where  $x=2$  

• 10

• 11

• 12

• 13

Derive  $\frac{\text{d}y}{\text{d}x}$  if $y=\left(3x^4-7\right)\left(5x^2+1\right)$ 

•  $12x^3\cdot10x$  

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

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

•  $\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$  (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

 $y=\frac{x+2}{x-3}$  Find  $\frac{dy}{dx}$  

•  $\frac{\left(x-3\right)-\left(x+2\right)}{\left(x-3\right)^2}$  

•   $\frac{\left(x+2\right)-\left(x-3\right)}{\left(x-3\right)^2}$  

•  $\frac{\left(x-3\right)-\left(x-2\right)}{\left(x+2\right)^2}$  

•  $\frac{\left(x+2\right)-\left(x-3\right)}{\left(x-3\right)^2}$  

 $y=\left(x^2+1\right)^5$  find  $\frac{dy}{dx}$  

•  $10\left(x^2+1\right)^4$  

•  $5\left(2x\right)^4$  

•  $5\left(x^2+1\right)^4$  

•  $10x\left(x^2+1\right)^4$  

Derive y=(Sin3x)²

• 2Cos(3x)

• 6cos(3x)

• 18xCos(3x)

• 6Cos(3x)Sin(3x)

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

What is the derivative of sin(x)?

• sin(x)
• cos(x)
• -sin(x)
• -cos(x)

What is the derivative of tan(x)?

• tan(x)
• sec(x)
• tan²(x)
• sec²(x)

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

• f'(x)
• y'
• dy
• dy/dx