# NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2

In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2 pdf, free NCERT solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.2 book pdf download.

## NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Exc  5.2

Differentiate the functions with respect to x in Questions 1 to 8.

Ex 5.2 Class 12 Maths Question 1.
sin(x² + 5)
Solution:
Let y = sin(x2 + 5),
put x² + 5 = t
y = sint
t = x²+5
$frac { dy }{ dx } =frac { dy }{ dt } .frac { dt }{ dx }$
$frac { dy }{ dx } =cost.frac { dt }{ dx } =cos({ x }^{ 2 }+5)frac { d }{ dx } ({ x }^{ 2 }+5)$
= cos (x² + 5) × 2x
= 2x cos (x² + 5)

Ex 5.2 Class 12 Maths Question 2.
cos (sin x)
Solution:
let y = cos (sin x)
put sinx = t
∴ y = cost,
t = sinx
$frac { dy }{ dx } =-sinquad t,frac { dt }{ dx } =cosquad x$
$frac { dy }{ dx } =frac { dy }{ dt } .frac { dt }{ dx } =(-sint)times cosx$
Putting the value of t, $frac { dy }{ dx } =-sin(sinx)times cosx$
$frac { dy }{ dx } =-[sin(sinx)]cosx$

Ex 5.2 Class 12 Maths Question 3.
sin(ax+b)
Solution:
let = sin(ax+b)
put ax+bx = t
∴ y = sint
t = ax+b
$frac { dy }{ dt } =cost,frac { dt }{ dx } =frac { d }{ dx } (ax+b)=a$
$Nowfrac { dy }{ dx } =frac { dy }{ dt } .frac { dt }{ dx } =costtimes a=acosquad t$
$frac { dy }{ dx } =acos(ax+b)$

Ex 5.2 Class 12 Maths Question 4.
sec(tan(√x))
Solution:
let y = sec(tan(√x))
by chain rule
$frac { dy }{ dx } =sec(tansqrt { x } )tan(tansqrt { x } )frac { d }{ dx } (tansqrt { x } )$
$frac { dy }{ dx } =sec(tansqrt { x } ).tan(tansqrt { x } ){ sec }^{ 2 }sqrt { x } .frac { 1 }{ 2sqrt { x } }$

Ex 5.2 Class 12 Maths Question 5.
$\ frac { sin(ax+b) }{ cos(cx+d) }$
Solution:
y = $\ frac { sin(ax+b) }{ cos(cx+d) }$ = $\ frac { v }{ u }$
u = sin(ax+b)

Ex 5.2 Class 12 Maths Question 6.
cos x³ . sin²(x5) = y(say)
Solution:
Let u = cos x³ and v = sin² x5,
put x³ = t

Ex 5.2 Class 12 Maths Question 7.
$2sqrt { cot({ x }^{ 2 }) } =y(say)$
Solution:
$2sqrt { cot({ x }^{ 2 }) } =y(say)$

Ex 5.2 Class 12 Maths Question 8.
cos(√x) = y(say)
Solution:
cos(√x) = y(say)
$frac { dy }{ dx } =frac { d }{ dx } cosleft( sqrt { x } right) =-sinsqrt { x } .frac { dsqrt { x } }{ dx }$
$=-sinsqrt { x } .frac { 1 }{ 2 } { (x) }^{ -frac { 1 }{ 2 } }=frac { -sinsqrt { x } }{ 2sqrt { x } }$

Ex 5.2 Class 12 Maths Question 9.
Prove that the function f given by f (x) = |x – 1|,x ∈ R is not differential at x = 1.
Solution:
The given function may be written as
$f(x)=begin{cases} x-1,quad ifquad xge 1 \ 1-x,quad ifquad x<1 end{cases}$
$R.H.Dquad atquad x=1quad =underset { hrightarrow 0 }{ lim } frac { f(1+h)-f(1) }{ h }$

Ex 5.2 Class 12 Maths 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:
(i) At x = 1
$R.H.D=underset { hrightarrow 0 }{ lim } frac { f(1+h)-f(1) }{ h }$

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