Derivative Rules
The Power Rule for Derivatives.
nx^{n-1}
Derivative of sinx
cosx
What does the graph of the derivative describe?
It shows all the slopes of lines tangent to the original graph
Find the antiderivative of x^2
x^3/3+c
The Constant Multiple Rule for Derivatives
(cf(x))' = cf'(x)
Derivative of tanx
sec2x
What does it mean when f'(x)= 0
A maximum, minimum, or critical point
What is reverse power rule?
1/(n+1)x^(n+1)
What is the product rule?
f'g+g'f
Derivative of cscx
-cscxcotx
How do you decided whether a critical point is a maximum or minimum?
Positive to negative = max; negative to positive =min
Find the antiderivative of sec^2(x)
tan(x)+c
What is the quotient rule?
f'g-g'f/ g2
Antiderivative of sinx
-cosx+C
What does it mean when f''(x)= 0
potential inflection point
Find the antiderivative of 1/x+3x^(1/2)
ln(x)+2x^(3/2)+c
Write the chain rule
(f’ º g) × g’
Antiderivative of csc^2(x).
-cot(x)+C
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
f''(x)=3x, f'(2)=1, f(4)=5
Find f(x)
f(x)=1/2x^3-5x-7