Grade 12 - Competition - Calculus

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

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

The derivative of a function is its

• Average Slope
• Maximum/Minimum
• Instantaneous rate of change
• Common Denominator

Find the second derivative of the following functions with respect to x.
y=3x⁴

• 36x²
• 12x³
• 4x³
• 12x²

Find the derivative. May leave answer with a rational exponent.

• 
• 
• 
• 

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Derive y=(x+2)(X-3)

• 2x-1

• 1

• x-6

• 2x

find 

• y = 2 x^-1
• y=2 x^-2
• y= −2x^-2
• y= −2 x^-1

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

What is the center and radius of this circle?
(x + 6)² + (y - 3)² = 36

• Center: (-6, -3)
   radius = 36
• Center: (6, -3)
   radius = 6
• Center: (6, 3)
   radius = 18
• Center: (-6, 3)
   radius = 6

Tags

CCSS.HSG.GPE.A.1

Simplify.
(6 + 7i)(7 + 7i)

• 5 + 105i
• -9 + 91i
• -7 + 91i
• 91 - 7i