The Power is Yours
What's the derivative of x4?
WHAT IS: 4x3
What rule would you use for f(x)=3x5?
WHAT IS: Power rule
Differentiate (x2+4)6
12x(x2+4)5
T/F: The derivative of a constant is 1.
WHAT IS: False; 0
What is the derivative of a constant?
WHAT IS: 0
What's the derivative of √x?
WHAT IS: 1/(2√x)
What rule would you use to differentiate f(x)=sin(x)ex?
WHAT IS: Product rule
Differentiate f(t)=(4t2-3t-3)-8
f"(t)=-8(4t2-3t-3)-9(8t-3)
T/F: The derivative of cos(x) is sin(x).
WHAT IS: False; -sin(x)
What does the derivative of a function represent?
WHAT IS: The slope of the tangent line OR the rate of change
BONUS: Why don't calculus majors throw house parties?
WHAT IS: Because you should never drink and derive!
What rule would you use for f(x)=ln(tan(x2))?
WHAT IS: Chain rule (twice!!!)
Differentiate e^(9x^2+7x+4)
(18x+7)e^(9x2+7x+4)
T/F: (f+g)'=f' + g'
WHAT IS: True
If f(x)=x2, what does f'(x)=?
WHAT IS: f'(x)=2x
What is the derivative of 1/(x4)?
WHAT IS: -4/x5
What rule would you use to differentiate f(x)=(x2+1)/(x-3)
WHAT IS: Quotient rule
Differentiate f(x)=sin(x3)
f'(x)=3x2cos(x3)
T/F: (fg)'=f'g'
What rule would you use to find the derivative of a product of two functions?
Differentiate [6x(5/3)-4x-2-12]
10x2/3+8x-3
What rule would you use for f(x)=tan(5x2)sin(x)
WHAT IS: Product rule and chain rule
Differentiate tan4(x4)
f'(x)=16x3tan3(x4)sec2(x4)
T/F: The derivative of |x| exists everywhere.
WHAT IS: False
For x>0 f'(x)=1
For x<0 f'(x)=-1
Since the left-hand and right-hand derivative do not match, the derivative does not exist at 0.
What symbol is often used to represent "the derivative"?
WHAT IS: f'(x) or dy/dx