Differentiation Class 11 OP Malhotra Exe-19A ISC Maths Ch-19 Solutions. In this article you would learn about Derivative of a Function and Geometrical Interpretation of (dy/dx). Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

Differentiation Class 11 OP Malhotra Exe-19A ISC Maths Solutions Ch-19

Board	ISC
Publications	S Chand
Subject	Maths
Class	11th
Chapter-19	Differentiation
Writer	O.P. Malhotra
Exe-19(A)	Derivative of a Function and Geometrical Interpretation of (dy/dx)

Derivative of a Function and Geometrical Interpretation of (dy/dx)

Differentiation Class 11 OP Malhotra Exe-19A ISC Maths Ch-19 Solutions.

Que-1: 2x

Sol: Let y = 2x …(1)
Let δx be the increment in x and corresponding increment in y be δy
∴ y + δy = 2 (x + δx) …(2)
subtracting eqn. (1) from eqn. (2); we get
δy = 2δx ; On dividing both sides by δx
∴ δy/δx = 2, Taking limits as δx → 0
Thus, Lt(δx→0) δy/δx = dy/dx = Lt(δx→0) = 2 = 2
∴ d/dx (2x) = 2

Que-2: (x – 1)²

Sol: Let y = f(x) = (x – 1)²
∴ f(x + δx) = (x + δx – 1)²
Thus by first principle, we have

Que-3: x³

Sol: Let y = f(x) = x³
∴ f (x + δx) = (x + δx)³
Then by first principle, we have

Que-4: 1/√x

Sol:

Que-5: √(x+1); x > – 1

Sol: Let y = f(x) = √(x+1) ∴ f(x + δx) = √(x+δx+1)
Then by first principle, we have

Que-6: 2x+3 / 3x+2

Sol: Let y = f(x) = (2x+3)/(3x+2)
∴ f(x + δx) = {2(x+δx)+3}/{3(x+δx)+2}
Then by first principle, we have

Que-7: 1 / √(x+a)

Sol: Given y = f(x) = 1/√(x+a)
∴f(x + δx) = 1/√(x+δx+a)
Then by first principle, we have

Que-8: x + 1/x

Sol: Let y = f(x) = x + (1/x)
∴f(x + δx) = (x + δx) + 1/(x+δx)
Then by first principle, we have

Que-9: 1 / √2x+3

Sol: Let y = f(x) = 1/√(2x+3)
∴ f (x + δx) = 1/√{2(x+δx)+3}
Then by first principle, we have

Que-10: 1 / x^(3/2)

Sol: Let y = f(x) = 1/x^(3/2)
∴ f(x + δx) = 1 / (x+δx)^(3/2)
Then by first principle, we have

Que-11: (x + 1) (2x – 3)

Sol: Let y = f(x) = (x + 1) (2x – 3)
∴f(x + δx) = (x + δx + 1) (2x – 3 + 2 δx)
Then by first principle, we have

Que-12: (x²+1)/x

Sol: Let y = f(x) = (x²+1)/x = x + (1/x)
∴f(x + δx) = (x + δx) + {1/(x+δx)}
Then by first principle, we have

–: End of Differentiation Class 11 OP Malhotra Exe-19A ISC Maths Ch-19 Solutions. :–

Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions

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