A full list of basic differentiation formulas have been provided below for the ease of students, so that they can find all the relevant differentiation formula(s) at one place.

It’s important to memorize the various formulas as it is the basis of the chapter “Differentiation”.

Here, we have provided various forms of differentiation formula(s) ranging from Power Functions, Trigonometric Functions, Exponential Functions etc.


Differentiation of a Power Function

Differentiation formulas

Where n is a fixed number, integer or rational.


Differentiation of a Constant Value

The differentiation of a constant value is always zero.


Differentiation of a Function multiplied with a constant

differentiation formulas 2


Differentiation of the Sum/Difference of Functions


Differentiation of the Product of Functions

If f(x) and g(x) are two differentiable functions then f(x).g(x) is also differentiable


Differentiation of the Quotient of Two Functions

If f(x) and g(x) are two differentiable functions and g(x)≠0 then f(x)/g(x) is also differentiable

Differentiation Formulas 3


Differentiation Formulas for Trigonometric Functions

Trigonometric functions can be defined as the functions of an angle of a triangle. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. To learn more about Trigonometry and its formulas check out Trigonometry Formula(s).

Differentiation Formulas 4


Differentiation Formulas for Inverse Trigonometric Functions

Inverse trigonometric functions are basically the inverse of the basic trigonometric functions i.e. sine, cosine, tangent, cotangent, secant, and cosecant functions. Differentiation of these inverse trigonometric functions are given below:

Differentiation Formulas 5


Exponential / Logarithmic Differentiation Formulas

Differentiation Formulas 6


Differentiation Formulas of Function of a Function

CHAIN RULE

If y = f(t) and t = g(x) then

Chain rule 1

This rule can be extended further.

If  y = f(t) and t = g(u) and u = h(x) then

Chain Rule 2


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