Show:
Basic Derivative Information and Power Rule
Chain Rule
Products & Quotients
Tangent lines
Trig Derivatives
100
The derivative calculates the ________.
Slope
100
Define the Chain Rule for f(g(x))
g′(x)f′(g(x))
100
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
100

The slope of the tangent line to the graph  y=f(x) through the point  x=x_0 is given by this limit.

lim_{h -> 0} (f(x_0+h)-f(x_0))/h

100
d/dx cosx=
-sinx
200

d/dx 5


0

200
d/dx (3x+1)²
6(3x+1)
200
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
200

If  f(3)=-2 and  f'(3)=4 , then the tangent line to  y=f(x) at  x=2 is given by this equation in slope intercept form.

y=4x-12

200
Differentiate y=tan(x)
y′ =sec²(x)
300
d/dx x² =
2x
300
d/dx sin(4x²)
8xcos(4x²)
300

d/dx [(x^3-8)/x]

2x+8/x^2

300

If tangent line to the graph  y=f(x) at  x=-2 is given by  y=5 , then  f'(-2) is this value.

0

300

d^73/dx^73 sin(x)

cos(x)

400
d/dx 3x²-x+3 =
6x-1
400

d/dx 1/(x^3-5x)

(5-3x^2)/(x^3-5x)^2

400

d/dx (x^5+7)(x^5-7)

10x^9

400

The tangent line through of a curve a point is the best ___________ to the curve at that point.

linear approximation

400

d/dx [6sin^2(x)+5cos^2(x)]

2 sin(x)cos(x)

500
Speed is _________.
the absolute value of velocity
500

d/dx (sin(x^2))^3


6 (sin(x^2))^2 cos(x^2)

500

f(x)= (x²-1)/(x²+1), what is f′(x)?

f′(x)= 4x/(x²+1)²

500

A function is not differentiable at  x=1 , but there is a tangent line through  x=1.  The tangent line has this property.

It is vertical (undefined slope).

500

d/dx [cot(x)]

-csc^2(x)