Derivatives
What's the Derivative?
f(x)=sin
f'(x) = cos(x)
y=(2x2+x)200
What would the inner function be?
I= 2x2+x
What is this rule called?
(f'g-g'f)/g2
Quotient Rule
What is the critical number of this function?
3(x-1)(x-3)
x=1, x=3
When a line lies BELOW tangent lines it is which concavity?
Concave Downward
What's the Derivative?
f(x)=cos(x)
f'(x) = − sin(x)
y= 1/(x3-2x2+7)4
What is the outer function for this equation?
O= 1/(x3-2x2+7)4
What is this rule called?
h(x) =f (g(x))g(x)
Chain Rule
What is the critical number of this function?
(1/4)-x=0
x= 1/4
When a line lies ABOVE tangent lines it is which concavity?
Concave upward
What's the Derivative?
f(x)=sec(x)
f'(x) = sec(x) tan(x)
I=x3
What is the derivative (aka I' ) of x3
I'=3x2
What is this rule called?
f(x) = c then f 0 (x) = 0
Constant Rule
What are the critical numbers of this function?
f'(x)= 3x2+12x-96
3(x+8)(x-4)=0
x=-8, x=4
When a line is increasing on a graph what is the equation?
f'(x)>0
What's the Derivative?
f(x)=tan(x)
f'(x) = sec2(x)
I= x2+1
What is the derivative of I.
I' = 2x
What is this rule called?
(xn)1=nxn-1
Power Rule
What are the critical numbers of this function?
f'(x)=15x4-15x2
15x2(x-1)(x+1)=0
x=0, x=1, x=-1
What is the derivative equation for decreasing on a graph?
f'(x)<0
What's the Derivative?
f(x)=cot(x)
f'(x) = − csc2(x)
f(x)=sin52x
How many inner functions will there be?
There will be 2 inner functions
I1=sin2x
I2=2x
What is this rule called?
g(x) = c · f(x) then g ·(x) = c · f 0 (x)
Constant Multiple Rule
What are the critical numbers of this function?
f'(x)= 4x3-16x
4x(x-4)(x+4)=0
x=0, x=4, x=-4
When a line on a graph is constant what is the equation?
f'(x)=0