Implicit, Related Rates, Optimization review

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

Tags

CCSS.HSF-IF.C.8B

Find dy/dx by Implicit Differentiation
9y + x = 4y

• 1/ 9
• 1/ 5
• -1/ 5 
• -1/ 9

Find dy/dx by Implicit Differentiation 
8x² + 16y² = 144

• x /2y
• x² / y
• −x /2y
• x² / y²

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx
xy+y²=2

• -y/(x+2y)
• y/(x+2y)
• -3y/x
• -3x/y

Find dy/dx by Implicit Differentiation
xy = 6

• -x/ y
• -y/ x
• -6y/ x
• y/x

What is the derivative of y³ with respect to x?

• 3y²
• 3y² (dy/dx)
• 3x²
• 3x² (dx/dy)

find dy²/ d²x   of   x² + y² = 16
Make sure to go as far as you can!

• -16/ y³
• (y² - x ^dy/dx) /  (y³)
• (y² - x²) / y³

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Tags

CCSS.8.G.B.8

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area of the outer circle changing when the diameter is 8 in?

• 80pi in/sec

• 20pi in/sec

• 60pi in/sec

• 40pi in/sec