Calculus Formula Sheet

Calculus is a branch in mathematics which deals with the study of limits, functions, derivatives, integrals, and infinite series. It has two main branches

• Differential calculus
• Integral calculus

It is a formula sheet which contains differentiation and integration formulas which are needed to solve the calculus problems. We should know all the calculus formulas before get into the problems. Calculus formula sheet helps you to learn all those formulas. It is very much helpful for the students at the time of examination for reviewing calculus formulas.

Integration is a limiting process which is used to find the area of a region under a curve.  We can also say that integration is an anti derivative of differentiation. Integration of a function is shown as,
int` f(x) dx = F(x) + C
int `  = Sign of integration
The variable x in dx is called variable of integration or integrator.
C= constant          

Differential calculus formula sheet:

Derivatives of polynomial functions:
`d/dx` (c) = 0
`d/dx` (x) = 1
`d/dx ` (cx) = c
`d/dx` (xⁿ) = nx^n-1
`d/dx` (cxⁿ) = ncx^n-1

Derivatives of trigonometric functions:
`d/dx` (sin x) = cos x
`d/dx` (cos x) =  - sin x
`d/dx ` (tan x) = sec² x
`d/dx` (cot x) = - cosec²x
`d/dx` (sec x) = sec x tan x
`d/dx` (cosec x) = - cosec x cot x

Derivatives of inverse trigonometric functions:
`d/dx` (sin^-1 x) = `1/sqrt(1 - x^2)`
`d/dx` (cos^-1 x) = - `1/sqrt(1 - x^2)`
`d/dx` (tan^-1 x) = `1/(1 + x^2)`
`d/dx` (sec^-1 x) = `1/(|x|sqrt(x^2 - 1))`
`d/dx` (cosec^-1 x) = - `1/(|x|sqrt(x^2 - 1))`
`d/dx` (cot^-1 x) = - `1/(1 + x^2)`

Derivatives of hyperbolic functions:
`d/dx` (sinh x) = cos hx
`d/dx ` (cosh x) = sin hx
`d/dx ` (tanh x) = sec h²x
`d/dx` (sech x) = - tanh x sech x
`d/dx` (cosech x) = - coth x cosech x
`d/dx` (coth x) = - cosech²x

Integral calculus formula sheet:

List of integrals of rational functions:
`int` k dx = kx + C
`int` x^a dx = `(x^(a+1))/(a+1)` + C
`int` 1/x dx = ln|x| + C

List of integrals of logarithmic functions:
`int` ln x dx = x ln x - x + C
`int ` log_ax dx = xlog_ax  - x(ln a) + C

List of integrals of exponential functions:
`int ` e^x dx = e^x + C
`int ` a^x dx = `(a^x)/(ln a)` + C

List of integrals of trigonometric functions:
`int` sin x dx = - cos x + C
`int` cos x dx  = sin x + C
`int` tan x dx  = - ln |cos x| + C
`int` cot x dx = ln |sin x| + C