Basic Derivative Information and Power Rule
The derivative calculates the ________.
Slope of the line
Define the Chain Rule for f(g(x))
g′(x)f′(g(x))
Define the Product Rule using f(x)g(x)
f′(x)g(x)+ g′(x)f(x)
Define the Quotient Rule using f(x)/g(x)
[g(x)f′(x) - f(x)g′(x)]/ (g(x))²
d/dx 5 =
0
d/dx (3x+1)²
6(3x+1)
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
Differentiate y= 2/(x+1)
y′ = -2/ (x+1)²
d/dx x² =
2x
d/dx sin(4x²)
8xcos(4x²)
Differentiate y=(x³-3x+2)(x2 + 2)
y′ =5x4 -3x2 +4x -6
Differentiate y= (1) / (x²)
y′= -2/x3
d/dx 3x²-x+3 =
6x-1
Differentiate y=(13x²-5x+8)2
y′ =676x3 -390x2 +466x-80
Differentiate y=x4cosx
y′ =4x3cos(x) - x4sin(x)
f(x)= (x²-1)/ x²+1, what is f′(x)?
f′(x)= [4x] / (x²+1)²
What is the definition of the derivative?
limit as h approaches zero of [f(x+h) -f(x)]/h
Differentiate y=3tan√x
y′ =3sec²√(x)/ 2√x
Differentiate y=x²sin(5x)
y′ =5x3cos(5x) + 3x2sin(5x)
Differentiate y= (x³)/(x+2)
y′ = [2x2(x + 3)]/ (x+2)²
d/dx sec(x)sin(x)=
sec2(x)