Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 5.2.
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NCERT Solutions for Maths Class 12 Exercise 5.1
NCERT Solutions for Maths Class 12 Exercise 5.3
NCERT Solutions for Maths Class 12 Exercise 5.4
NCERT Solutions for Maths Class 12 Exercise 5.5
NCERT Solutions for Maths Class 12 Exercise 5.6
NCERT Solutions for Maths Class 12 Exercise 5.7
NCERT Solutions for Maths Class 12 Exercise 5.2
Differentiate the
functions with respect to x in Questions 1 to 8.
Maths Class 12 Ex 5.2 Question 1.
sin (x² + 5)Solution:
Let y = sin (x2
+ 5),
Put x² + 5 = t
Then, y = sin t
= cos (x² + 5) × 2x
= 2x cos (x² + 5)
Maths Class 12 Ex 5.2 Question 2.
cos (sin x)Solution:
Let y = cos (sin
x)
Put sin x = t
∴ y = cos t, where t = sin x
Maths Class 12 Ex 5.2 Question 3.
sin (ax + b)Solution:
Let y = sin (ax + b)
Put ax + b = t
∴ y = sin t, where t = ax + b
Maths Class 12 Ex 5.2 Question 4.
sec (tan (√x))Solution:
Let y = sec (tan (√x))
By chain rule,
Maths Class 12 Ex 5.2 Question 5.
Solution:
Maths Class 12 Ex 5.2 Question 6.
cos x³ . sin² (x5)Solution:
Let y = cos x³ .
sin² (x5)
Maths Class 12 Ex 5.2 Question 7.
Solution:
Maths Class 12 Ex 5.2 Question 8.
cos (√x)
Solution:
Maths Class 12 Ex 5.2 Question 9.
Prove that the function f given by f(x) = |x – 1|, x ∈ R is not differentiable at x = 1.Solution:
We have f(x) = |x – 1|,
x ∈ R
It is known that a
function f is
differentiable at a point x = c in its
domain if both LHD and RHD are finite and equal.
To check the differentiability of the
given function at x = 1,
Since LHD and RHD
at x = 1 are
not equal,
Therefore, f is not differentiable
at x = 1.
Maths Class 12 Ex 5.2 Question 10.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differential at x = 1 and x = 2.Solution:
We have f(x) = [x], 0
< x < 3
It is known that a function f is
differentiable at a point x = c in its
domain if both LHD and RHD are finite and equal.
To check the differentiability of the
given function at x = 1,
Since LHD and RHD
at x = 1 are
not equal,
Therefore, f is not
differentiable at x = 1.
Similarly, f is not
differentiable at x = 2.
Related Links:
NCERT Solutions for Maths Class 12 Exercise 5.1
NCERT Solutions for Maths Class 12 Exercise 5.3
NCERT Solutions for Maths Class 12 Exercise 5.4
NCERT Solutions for Maths Class 12 Exercise 5.5