CLASS – 12TH (CBSE)
FORMULA SHEET OF DIFFERENTIATION
ALGEBRAIC –
d (UV ) dV dV
dx
= U
dx + V dx Product rule
U dU dV
d( ) V −U
V = dx
2
dx Quotient rule
dx V
d (U ±V ) dU dV
dx
= ±
dx dx Addition and subtraction
d xn d (constant )
dx
= nxn-1 dx
= 0
d (K . f ( x )) d (f ( x ) )
dx
= K dx
where K is constant.
TRIGONOMETRY FUNCTION –
sin(x) = cos(x) tan(x) = sec2(x) sec(x) = sec(x).cosec(x)
cos(x) = -sin(x) cot(x) = -cosec2(x) cosec(x) = cosec(x).cot(x)
INVERSE OF TRIGONOMETRICB FUNCTION –
1 1 1
sin-1(x) = √1−x 2 tan-1(x) = 1+ x
2 sec-1(x) = ¿ x∨√ x 2−1
−1 −1 −1
cos-1(x) = √1−x 2 cot-1(x) = 1+ x2
cosec-1(x) = ¿ x∨√ x 2−1
( jinke starting m C h unke differentiation m minus ata h )
LOGARTHMIC AND EXPONENTIAL FUNCTION –
FORMULA SHEET OF DIFFERENTIATION
ALGEBRAIC –
d (UV ) dV dV
dx
= U
dx + V dx Product rule
U dU dV
d( ) V −U
V = dx
2
dx Quotient rule
dx V
d (U ±V ) dU dV
dx
= ±
dx dx Addition and subtraction
d xn d (constant )
dx
= nxn-1 dx
= 0
d (K . f ( x )) d (f ( x ) )
dx
= K dx
where K is constant.
TRIGONOMETRY FUNCTION –
sin(x) = cos(x) tan(x) = sec2(x) sec(x) = sec(x).cosec(x)
cos(x) = -sin(x) cot(x) = -cosec2(x) cosec(x) = cosec(x).cot(x)
INVERSE OF TRIGONOMETRICB FUNCTION –
1 1 1
sin-1(x) = √1−x 2 tan-1(x) = 1+ x
2 sec-1(x) = ¿ x∨√ x 2−1
−1 −1 −1
cos-1(x) = √1−x 2 cot-1(x) = 1+ x2
cosec-1(x) = ¿ x∨√ x 2−1
( jinke starting m C h unke differentiation m minus ata h )
LOGARTHMIC AND EXPONENTIAL FUNCTION –
