NCERT Solutions for Chapter 5 Continuity and Differentiability Class 12 Maths Exercise 5.4

Class 12 Maths NCERT Solutions for Chapter 5 Continuity and Differentiability Exercise 5.4

Continuity and Differentiability Exercise 5.4 Solutions

1. Differentiate the following w.r.t. x :
e^x /sin x

Solution

Let y = e^x /sin x
By using the quotient rule, we obtain 

2. Differentiate the following w.r.t. x : e^{sin-1 x}

Solution

Let y = e^sin-1 x
By using the chain rule, we obtain 

3. Differentiate the following w.r.t. x: e^x3 

Solution

Let y = e^x3 
By using the chain rule, we obtain

4. Differentiate the following w.r.t. x : 
sin(tan-1 e^-x )

Solution

Let y = sin(tan-1 e^-x )
By using the chain rule, we obtain 

5. Differentiate the following w.r.t. x :
log(cos e^x )

Solution

Let y = log(cos e^x )
By using the chain rule, we obtain

6. Differentiate the following w.r.t. x : 

e^x + e^x2 + e^x3

Solution

7. Differentiate the following w.r.t. x : 

Solution

Let y = 
y² = e^√x
By differentiating this relationship with respect to x, we obtain
y² = e^√x

8. Differentiate the following w.r.t. x : log (log x), x > 1 

Solution

Let y = log (log x) 
By using the chain rule, we obtain 

9. Differentiate the following w.r.t. x :

cos x/log x , x > 0

Solution

Let y = cos x/log x
By using the quotient rule, we obtain 

10. Differentiate the following w.r.t. x : 

cos (log x + e^x ), x > 0 

Solution

Let y = cos (log x + e^x )
By using the chain rule, we obtain