Chapter 2 Differentiation

The first principle differentiation 

 $y=x^2-3$  

is

•  $\lim_{h\rightarrow0}\ \frac{\left(x^2-3+h\right)-x^2-3}{h}$  

•  $\lim_{h\rightarrow0}\ \frac{\left(x^2-h-3\right)-x^2+3}{h}$  

•  $\lim_{h\rightarrow0}\ \frac{\left(\left(x+h\right)^2-3\right)-\left(x^2-3\right)}{h}$  

•  $\lim_{h\rightarrow0}\ \frac{\left(x^2+h-3\right)-\left(x^2-3\right)}{h}$  

 $\lim_{h\rightarrow0}\ \frac{2\left(x+h\right)-2x}{h}$  is

• 0

• 1

• 2

• does not exist

• 3x²
• x³
• 6x
• 3x² + x³

Tags

CCSS.6.EE.A.4

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

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

Tags

CCSS.HSA.APR.A.1

Differentiate      y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

Differentiate with respect to x...

• 16x + 4x^-2

• 16x - 4x^-2

• 16x + 4x

• 16x - 4x

Tags

CCSS.HSA.APR.A.1

Differentiate with respect to x...

• 4x - 5

• 4x - 3

• 2x - 5

• 2x - 3

Tags

CCSS.HSA.APR.A.1

What rule should be used in deriving h(x) = 2(x - 4)³

• Power rule

• Product rule

• Quotient rule