Differentiation Formulas

Q1

What are the formulas of differentiation?

The formulas of differentiation that helps in solving various differential equations include:
Derivatives of basic functions
Derivatives of Logarithmic and Exponential functions
Derivatives of Trigonometric functions
Derivatives of Inverse trigonometric functions
Differentiation rules

Q2

What are the basic rules of differentiation?

The basic rule of differentiation are:
Power Rule: (d/dx) (xⁿ ) = nx^{n-1}
Sum Rule: (d/dx) (f ± g) = f’ ± g’
Product Rule: (d/dx) (fg)= fg’ + gf’
Quotient Rule: (d/dx) (f/g) = [(gf’ – fg’)/g²]

Q3

What are the derivatives of trigonometric functions?

The derivatives of six trigonometric functions are:
(d/dx) sin x = cos x
(d/dx) cos x = -sin x
(d/dx) tan x = sec² x
(d/dx) cosec x = -cosec x cot x
(d/dx) sec x = sec x tan x
(d/dx) cot x = -cosec² x

Q4

What is d/dx?

The general representation of the derivative is d/dx. This denotes the differentiation with respect to the variable x.

Q5

What is a UV formula?

(d/dx)(uv) = v(du/dx) + u(dv/dx)
This formula is used to find the derivative of the product of two functions.