Question

Maths formula for differential calculus

Answer 1

Basic Formulas

Suppose we have two function of 'x' that is 'u' and 'v', where 'a' and 'n' are constants, and 'd' is the differential operator.

Linearity rule: (d/dx) (a u) = a (du/dx)

Addition rule: (d/dx) (u+v) = du/dx + dv/dx

Subtraction rule: (d/dx) (u -v) = du/dx – dv/dx

Product rule: (d/dx) (u *v)= u dv/dx + v du/dx

Quotient rule :( d/dx) (u/v) = (v du/dx – u dv/dx)/v2

Let’s see the basic function based formula:

Basic Functions :( d/dx) a =0

(d/dx) x=1

(d/dx) xn = n x n-1

(d/dx) |x| = x/|x|, x! =0

(d/dx) e x =e x

(d/dx) ax = (ln a) ax (a>0)

(d/dx) ln x = 1/x

Trigonometry function:

(d/dx) sin x =cos x

(d/dx) cos x = -sin x

(d/dx) tan x = sec2 x

(d/dx) cot x = -cosec 2 x

(d/dx) sec x = sec x tan x

(d/dx) cosec x = -cosec x cot x

(d/dx) arcsin x = sin-1 x =1/√ (1-x2)

(d/dx) arccos x = cos-1 x =-1/√ (1-x2)

(d/dx) arctan x = tan-1 x =1/ (1 +x2)

(d/dx) arccot x = cot-1 x =-1/ (1+x2)

(d/dx) arcsec x = sec-1 x =1/ [|x|√ (x2 -1)]

(d/dx) arccosec x = cosec-1 x =-1/ [|x|√ (x2 -1)]