Page 7 - Formula-All

B. Tech. Semester-I (All Branch) Important Formulas
Differentiation Formula

(A) Basic Algebraic:

d
n
(1) [x ] = nx n−1
dx

d
(2) [C] = 0 ; where C is constant
dx

d d
(3) [Cf(x)] = C [f(x)] ; where C is constant
dx dx

d d d
(4) [f(x) + g(x)] = f(x) + g(x)
dx dx dx

d d d
(5) [f(x) − g(x)] = f(x) − g(x)
dx dx dx

d d d
(6) [f(x) · g(x)] = f(x) · g(x) + g(x) · f(x)
dx dx dx

d d
g(x) · f(x) − f(x) · g(x)
d f(x) dx dx
(7) =
dx g(x) [g(x)] 2

(B) Logarithmic Functions:

d 1
(1) [log x] =
dx x

d 1
(2) [log 5x] = · (5)
dx 5x

(C) Exponential Functions:

d
x
(1) [e ] = e x
dx

d 5x 5x
(2) e = e · (5)
dx

d
x
x
(3) [a ] = a · log a
dx

Mr. Snehal D. Patel (Assistant Professor - Mathematics) Page 4 of 9