Derivative Rules
f(x) = c then f'(x) = 0
f(x) = sin(x) then f'(x)=
∫a dx
ax + C
∫xn dx
xn+1 / n+1 + C
What is the area of a Triangle?
1/2bh
What is the product rule?
First X Derivative of the Second + Second X Derivative of the First
f(x) = cos(x) then f' (x)=
-sin(x)
∫x dx
x2/2 + C
What is the Intermediate Value Theorem?
A function y= f(x) that is continuous on a closed interval [a,b] takes on every value between f(a) and f(b).
What is the area of a Trapezoid?
h/2(a+b)
What is the Power Rule?
f(x) =xn then f'(x) = nxn-1
f(x) = tan(x) then f'(x) =
sec2(x)
∫x2 dx
x3/3 + C
d/dx [cot u]
-(csc2 u)
What is the Area and Circumference of a Circle?
Area= πr2
Circumference= 2πr
What is the Quotient Rule?
Bottom X Derivative of the Top - Top X Derivative of the Bottom OVER Bottom Squared
f(x) = sec(x) then f'(x)
sec(x) tan(x)
∫sec2(x) dx
tan(x) + C
d/dx [csc u] =
-(csc u cot u)
What is the Volume of a Cone?
Ah/3
What is the Chain rule?
f(g(x)) = f'(g(x))⋅g'(x)
f(x) = cot(x) then f'(x) =
− csc2 (x)
∫ax dx
ax/ln(a) + C
d/dx [ln u]
u'/u
Volume= 4/3πr3
Surface Area= 4πr2