Calculus Formulas and Derivatives
volume of a cube
V = s³
volume of a cone
V = ¹/₃ π r²h
volume of a cylinder
V = π r^2 h
volume of a sphere
V = ⁴/₃π r³
pythagorean theorem
a² + b² = c²
derivative of the area of a circle
dA/dt = 2πr dr/dt
derivative of the area of a square
da/dt = 2s ds/dt
derivative of the area of a rectangle
da/dt = l dw/dt + w dl/dt
derivative of the area of a right triangle
da/dt = ½ (b dh/dt + h db/dt)
derivative of the area of an equilateral triangle
da/dt = √3/4 (2s ds/dt)
derivative of the circumference of a circle
dc/dt = 2π dr/dt
derivative of the perimeter of a rectangle
dp/dt = 2 dl/dt + 2 dw/dt
derivative of the perimeter of a square
dp/dt = 4 ds/dt
derivative of the sa of a cube
ds/dt = 12s ds/dt
derivative of the sa of a cylinder
ds/dt = 2π(r dh/dt + h dr/dt)
derivative of the sa of a sphere
ds/dt = 4π(2r dr/dt)
derivative of the volume of a cube
dv/dt = 3s²
derivative of the volume of a cone
dv/dt = ¹/₃π(2rh dr/dt + r² dh/dt)
derivative of the volume of a cylinder
dv/dt = π(r² dh/dt + 2r dr/dt h)
derivative of the volume of a sphere
dv/dt = ⁴/₃π (3r² dr/dt)
slant height of a triangle
l² + 6² = h²
circle
x² + y² = 25
derivative of the pythagorean theorem
2a da/dt + 2b db/dt = 2c dc/dt
derivative of the slant height of a triangle
2l dl/dt = 2h dh/dt
derivative of a circle
2x dx/dt + 2y dy/dt = 0
area of a square
A = s²
area of an equilateral triangle
A = s²√3 / 4
area of a right triangle
A = ½bh
area of a circle
A = π r²
area of a rectangle
A= l w
circumference of a circle
C = 2π r
perimeter of a rectangle
P = 2l + 2w
perimeter of a square
P = 4s
sa of a cylinder
S = 2π rh+2πr
sa of a sphere
S = 4π r²
sa of a cube
S = 6s²