Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

Tags

CCSS.HSS.ID.C.7

The derivative of a function is its

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

Tags

CCSS.HSF.IF.B.4

f'(x)=

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

• $\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

• $\frac{\text{d}y}{\text{d}x}$

• an equation for the slope of the tangent line

If

 $f\left(x\right)=x^2+2x$  which of the following is the derivative of f(x)

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

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

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

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

Answer explanation

this is the limit definition of taking a derivative

 $\frac{d}{dx}\left(\frac{\sin x}{1+\cos x}\right)=$  

•  $\frac{\cos x}{-\sin x}$  

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

•  $\frac{1}{1+\cos x}$  

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

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.IF.C.8

The function shown

• is continuous at x = 8

• is differentiable at x = 8

• has a limit that exists at x = 8

• exists at x = 8

Tags

CCSS.HSF.IF.A.2

The function shown

• is continuous at x = 2

• is differentiable at x = 2

• has a limit that exists at x = 2

• exists at x = 2

The function shown

• is continuous at x = 0

• is differentiable at x = 0

• has a limit that exists at x = 0

• exists at x = 0

Which graph is the derivative of the top graph?

• A
• B
• C
• D

f' is given, which could be f?

• A
• B
• C

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11