# NCERT solution class 12 chapter 5 Continuity and Differentiability exercise 5.3 mathematics part 1

## EXERCISE 5.3

#### Question 1:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain #### Question 2:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain  #### Question 3:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain Using chain rule, we obtain and From (1) and (2), we obtain #### Question 4:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain #### Question 5:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain  [Derivative of constant function is 0] #### Question 6:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain #### Question 7:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain Using chain rule, we obtain From (1), (2), and (3), we obtain #### Question 8:

Find : The given relationship is Differentiating this relationship with respect to x, we obtain #### Question 9:

Find : We have,y = sin-12×1 + x2put x = tan θ ⇒ θ = tan-1xNow,    y = sin-12 tan θ1 + tan2θ⇒y = sin-1sin 2θ, as sin 2θ=2 tan θ1 + tan2θ⇒y = 2θ,  as sin-1sin x=x⇒y = 2 tan-1x⇒dydx = 2 × 11 + x2, because dtan-1xdx=11 + x2⇒dydx = 21 + x2

#### Question 10:

Find : The given relationship is  It is known that, Comparing equations (1) and (2), we obtain Differentiating this relationship with respect to x, we obtain #### Question 11:

Find : The given relationship is, On comparing L.H.S. and R.H.S. of the above relationship, we obtain Differentiating this relationship with respect to x, we obtain

sec2y2.ddxy2=ddxx

⇒sec2y2×12dydx=1

⇒dydx=2sec2y2

⇒dydx=21+tan2y2

dydx=21+x2

#### Question 12:

Find : The given relationship is   Differentiating this relationship with respect to x, we obtain Using chain rule, we obtain   From (1), (2), and (3), we obtain Alternate method    Differentiating this relationship with respect to x, we obtain #### Question 13:

Find : The given relationship is  Differentiating this relationship with respect to x, we obtain  #### Question 14:

Find : The given relationship is  Differentiating this relationship with respect to x, we obtain #### Question 15:

Find : The given relationship is   Differentiating this relationship with respect to x, we obtain error: Content is protected !! 