Basics
What is the derivative of f(x)=x7?
7x6
What does a derivative represent on a graph?
The slope of a function at different points along its curve
Find the derivative of f(x)= x (cos(x))
What rule did you use?
f'(x)= cos(x)- x sin (x)
product rule
Differentiate f(x)=sin(x2)
f'(x)=2xcos(x2)
If s(t)=t6 what is the velocity?
v(t)=s'(t)=6t5
What is the derivative of f(x)=5x-7?
5
If a function is increasing the derivative is ...
Positive
find the derivative f(x)= 1/x
What rule did you use?
f'(x)= -1/x2
quotient rule
differentiate f(x)=ln(2x2+5)
f'(x)=4x/2x2+5
Find the acceleration if v(t)= 6t-4
a(t)=v'(t)=6
What is the derivative of f(x)=3x4-2x3+5x+8 ?
12x3 -6x2+5
If the functions graph is concaved down the second derivative is ...
f"(x) < 0
find the derivative of f(x)= (x2+2)/(x-1)
What rule did you use?
f'(x)=(2x)(x-1)-(x2+2)(1)/(x-1)2
Quotient rule
find dy/dx if y=sin(x2+3x)
dy/dx=cos(x2+3x)(2x+3)
If a function has a critical point at x=3 what must be true?
f'(3)= 0 or undefined
Find the derivative of f(x)=5ex + 3ln(x) ?
5ex+ 3/x
It has a local min at x=2
find the derivative of f(x)=x2(ln(x))
What rule did you use?
f'(x)=2xln(x)+x
product rule
differentiate f(x)=ln(sin(x)-cot(x))
1/sin(x)-cot(x)
If a particle changed direction, what happens to the velocity?
Velocity must change signs
What is the derivative of f(x)=tan(x) + sec(x)?
sec2(x)+sec(x)tan(x)
A graph of a function is decreasing and concaved up. What does that say about f' and f"?
f'(x)<0 and f"(x)>0
if f(2)=-8,f'(2)=3,g(2)=17 and g'(2)=-4 determine the value of (f g)' 2
(f g)'(2)=(3)(17)+(-8)(-4)=83
differentiate f(x)=2sin(3x+tan(x))
f'(x)=2(3+sec2(x))cos (3x+tan(x))
The position of the car is s(t)=t3 -6t+9t. Find the velocity at t=2
velocity at t=2 is 15