Derivative (chain rule, ln, e, implicit differentiation)

Find the first derivative of  $y=\left(x^3+19\right)^7$  

•  $\frac{\text{d}y}{\text{d}x}=21x^2\left(x^3+19\right)^6$  

•  $\frac{\text{d}y}{\text{d}x}=21x^3\left(x^3+19\right)^6$  

•  $\frac{\text{d}y}{\text{d}x}=3x^2\left(x^3+19\right)^6$  

•  $\frac{\text{d}y}{\text{d}x}=7x^2\left(x^3+19\right)^6$  

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 6x(x² + 1)²
• dy/dx = 2x(x² + 1)²

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Find the derivative:  $y=3\ln\left(x^2-3\right)$   

•  $\frac{6x}{x^2-3}$  
  

•  $\frac{3}{x^2-3}$  
  

•  $\frac{3x}{x^2-3}$  
  

•  $\frac{9x}{x^2-3}$  
  

 $f\left(x\right)=\frac{1}{x-1}$  

What is the derivative of f?

•  $\frac{1}{\left(x-1\right)^{-1}}$  
  

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

•  $-\frac{1}{x-1}$  
  

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

If $x^3+y^3=36$ , then find  $\frac{dy}{dx}$   by Implicit Differentiation. 

•  $6-x$  

•  $3x^2+3y^2$  
  

•  $-\frac{x^2}{y^2}$  
  

•  $0$  
  

Find   $\frac{dy}{dx}$  :  $2x^2-3y^2=4$  

•  $\frac{2x}{y}$  

•  $\frac{x}{3y}$  

•  $\frac{3y}{2x}$  

•  $\frac{2x}{3y}$  

Find  $\frac{dy}{dx}$  by Implicit Differentiation for $xy=6$ . 

•  $-\frac{x}{y}$  
  

•  $-\frac{y}{x}$  
  

•  $-\frac{6y}{x}$  
  

•  $\frac{y}{x}$  
  

Find dy/dx at the given point

 $x^3+2xy-y^2=11\$  at  $\left(2,\ 3\right)$  

•  $-\frac{4}{7}$  
  

• 12

• -9

• 9

Find  $\frac{dy}{dx}$  for  $y=e^{-5x^5}$  .

•  $e^{-5x^5}$  

•  $-5e^{-5x^5}$  
  

•  $-25x^4e^{-5x^5}$  
  

•  $\ln\left(-5x^5\right)$  
  

Tags

CCSS.HSF-IF.C.8B