Chain Rule, Implicit Diff, Higher Order, & L'Hopital

When do you use the chain rule?

• anytime you want
• when there is a function in a function
• where there are multiple layers to a lasagna (yum)
• when there is division

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

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Tags

CCSS.HSA.APR.A.1

Find the derivative of:
f(x) = 7(3x + 4)⁵

• 35(3x + 4)⁵
• 35(3x + 4)⁴
• 105(3x + 4)⁵
• 105(3x + 4)⁴

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Tags

CCSS.HSA.REI.A.2

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)

Find dy/dx by Implicit Differentiation 
x + 4y = 1

• -1/4
• -1 
• 4
• 1 

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

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx by Implicit Differentiation
xy = 6

• -x/ y
• -y/ x
• -6y/ x
• y/x

Find dy/dx
xy+y²=2

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