NCERT Class 12 Maths
Chapter 5: Continuity And Differentiability
10 Questions Solved
NCERT Solutions for Class 12 Maths Chapter 5 Continuity And Differentiability — Exercise 5.2
Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.
Question 1
Differentiate \(\sin{\left(x^{2} + 5 \right)}\) with respect to x; on R.
Question 2
Differentiate \(\cos{\left(\sin{\left(x \right)} \right)}\) with respect to x; on R.
Question 3
Differentiate \(\sin{\left(a x + b \right)}\) with respect to x; on R.
Question 4
Differentiate \(\sec{\left(\tan{\left(\sqrt{x} \right)} \right)}\) with respect to x; where x>0 and tan(√x), sec(tan(√x)) are defined.
Question 5
Differentiate \(\frac{\sin{\left(a x + b \right)}}{\cos{\left(c x + d \right)}}\) with respect to x; where the denominator cos(cx+d)…
Question 6
Differentiate \(\sin^{2}{\left(x^{5} \right)} \cos{\left(x^{3} \right)}\) with respect to x; on R.
Question 7
Differentiate \(2 \sqrt{\cot{\left(x^{2} \right)}}\) with respect to x; where cot(x²)>0 and sin(x²)≠0.
Question 8
Differentiate \(\cos{\left(\sqrt{x} \right)}\) with respect to x; for x>0 (the right derivative at x=0 is −1/2).
Question 9
Prove f(x)=|x−1| is not differentiable at x=1.
Question 10
Prove f(x)=⌊x⌋, 0<x<3, is not differentiable at x=1,2.