Q1Written answer
Find the derivative of x2– 2 at x = 10.
Show solutionHide solution
Worked solution
Let f (x) = x2 – 2
NCERT · Class 11 · Maths
Chapter 13: Limits and Derivatives Exercise 13.2
Practice each question, then open the answer or worked solution.
Questions
11 questionsQ2Written answer
Find the derivative of x at x = 1.
Show solutionHide solution
Worked solution
Let f (x) = x
Then,
Q3Written answer
Find the derivative of 99x at x = l00.
Show solutionHide solution
Worked solution
Let f (x) = 99x,
From the first principle,
= 99
Q4Written answer
Find the derivative of the following functions from the first principle.
(i) x3 – 27
(ii) (x – 1) (x – 2)
(iii) 1 / x2
(iv) x + 1 / x – 1
Show solutionHide solution
Worked solution
(i) Let f (x) = x3 – 27
From the first principle,
(ii) Let f (x) = (x – 1) (x – 2)
From the first principle,
(iii) Let f (x) = 1 / x2
From the first principle, we get
(iv) Let f (x) = x + 1 / x – 1
From the first principle, we get
Q5Written answer
For the function 
, prove that f’ (1) =100 f’ (0).
Show solutionHide solution
Worked solution
Q6Written answer
Find the derivative of 
for some fixed real number a.
Show solutionHide solution
Worked solution
Q7Written answer
For some constants a and b, find the derivative of
(i) (x − a) (x − b)
(ii) (ax2 + b)2
(iii) x – a / x – b
Show solutionHide solution
Worked solution
(i) (x – a) (x – b)
(ii) (ax2 + b)2
= 4ax (ax2 + b)
(iii) x – a / x – b
Q8Written answer
Find the derivative of 
for some constant a.
Show solutionHide solution
Worked solution
Q9Written answer
Find the derivative of
(i) 2x – 3 / 4
(ii) (5x3 + 3x – 1) (x – 1)
(iii) x-3 (5 + 3x)
(iv) x5 (3 – 6x-9)
(v) x-4 (3 – 4x-5)
(vi) (2 / x + 1) – x2 / 3x – 1
Show solutionHide solution
Worked solution
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Q10Written answer
Find the derivative of cos x from the first principle.
Show solutionHide solution
Worked solution
