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Related Rates Equations


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A = π(r²)
Area of a Circle
V = π (r²)h
Volume of a Cylinder
Pythagorean Theorem
in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs
S = 2π(r)(h) + 2π(r²)
Surface Area of a Cylinder
A = s²
Area of a square
S = 4π(r²)
Surface Area of a Sphere
Perimeter of a rectangle
P = 2l + 2w
V = 1/3π(r²)h
Volume of a Cone
V = s³
Volume of a cube
x² + y² = 25
x² + y² = 1 Circle
C = 2π(r)
Circumference of a Circle
V = 4/3π(r²)
Volume of a Sphere
P = 4s
Perimeter of a Square
A = lw
Area of a Rectangle
A = 1/2bh
Area of a Triangle
A = (s²√3)/4
Area of an Equilateral Triangle
V=(4/3)πr³
Volume of a Sphere
SA=4πr²
Surface Area of a Sphere
V=πr²h
Volume of a Circular Cylinder
SA=2πr²+2πr²h
Surface Area of a Cylinder
V=(1/3)πr²h
Volume of a Circular Cone
SA=πr√(r²+h²)
Surface Area of a Cone
e^x
ƒ'(x) of e^x
1/x
d/dx ln|x|
cos(x)
d/dx sin(x)
-sin(x)
d/dx cos(x)
sec²(x)
d/dx tan(x)
-csc(x)cot(x)
Derivative of csc(x)
sec(x)tan(x)
d/dx sec(x)
-csc²(x)
d/dx cot(x)
1/√(1-x²)
d/dx arcsin(x)
-1/√(1-x²)
d/dx arccos(x)
1/(1+x²)
d/dx arctan(x)
a^xln(a)
d/dx a^x
f'(x)g(x)+g'(x)f(x)
Product Rule
Quotient Rule
y = ln(x)/x², state rule used to find derivative
f'(g(x))g'(x)
Chain Rule
sin²(x)+cos²(x)
1
1+tan²(x)=
sec²(x)
sin(2x)=
2sin(x)cos(x)
cos(2x)=
cos²(x)-sin²(x)
cos²(x)-sin²(x)=
2cos²(x)-1
2cos²(x)-1=
1-2sin²(x)
1/x
d/dx ln(x)
x^a+b
x^a +x^b
(x^a)^b
x^ab
lnx
1/x
ln(ab)
ln(a)+ln(b)
ln(a^b)
bln(a)
ln(1/a)
-ln(a)
e^lnx
x
Ln(e^x)
x
ln(e)
1, when x is 0 or 1
ln (1)
0, when x is 0 or 1
-b±√(b²-4ac)/2a
quadratic equation
x²/x³
x²⁻³=x⁻¹
sin(a)cos(b)+cos(a)sin(b)
sin (a+b)
cos(a+b)
cos(a)cos(b)-sin(a)sin(b)
cos²(x)
1+cos(2x)/2
sin²(x)
1-cos(2x)/2
y=x²+2 movement
moves parabola up 2
y=(x-3)²
moves graph right 3
1
lim as x->0 sin(x)/x
x^n =nx^n−1
State the differentiation rule both in symbols and rules The Power Rule
cf =cf'
Constant Multiple Rule
Sum Rule
f + g=f' + g'
Difference Rule
f - g =f' − g'
Product Rule
y = x cos(x), state rule used to find derivative
f(g(x))=f'(g(x))g'(x)
Chain Rule
V=x³
Volume of a Cube
A=pir^2
Area of a Circle
A=x^2
Area of a Square
A=w*l
Area of a Rectangle
5/(1/5)
25
ln(sin(x))'
cot(x)
ln(cos(x))'
-tan(x)
ln(tan(x))'
sin(θ)/cos³(x)
ln(sec(θ))'
tan(θ)
ln(cot(x))'
cos(x)/sin³(x)
ln(csc(x))'
-cot(x)
4πr²
SA of Sphere
4/3 πr³
Volume of a sphere
A=πr²
Area formula with radius
1/3 πr²h
Volume of a cone
V=s³
volume of a cube
(1/2)b*h*w
volume of a prism
πr²h
V of cylinder