Continuity & Differentiability(Ex. 5.4)

 Exercise 5.4

Differentiate the following w.r.t. x:

Solun:- Let

Differentiate w.r.t. x:-

We know that:-

,x ≠ nπ, n ∈ Z

2. e

Solun:- Let

Differentiate w.r.t. x:-

, x ∈ (-1, 1)

3. e

Solun:- Let y = e

Differentiate w.r.t. x:-

dy/dx = d( e)/dx

dy/dx = e.d(x3)/dx

dy/dx = 3x2.e

4. sin (tan-1 e-x)

Solun:- Let y = sin (tan-1 e-x)

Differentiate w.r.t. x:-

dy/dx = d[sin(tan-1 e-x)] / dx

dy/dx = cos(tan-1 e-x).d[tan-1 e-x]/dx

We know that:-

5. log (cos ex)

Solun:- Let y = log (cos ex)

Differentiate w.r.t. x:-

6. ex + e+.......e

Solun:- Let y = ex + e + e + e + e

Differentiate w.r.t. x:-

dy/dx = d(ex)/dx+d(e)/dx+d(e)/dx+d(e)/dx+d(e)/dx

dy/dx = ex + 2xe+ 3x2e+ 4x3e+ 5x4e

7.

Solun:- Let y =

Differentiate w.r.t. x:-

, x>0

8. log (log x) , x > 1

Solun:- Let y = log (log x)

Differentiate w.r.t. x:-

,

9. ,

Solun:- Let y = cos x / log x

Differentiate w.r.t. x:-

We know that:-

,x>0

10. cos (log x + ex) , x > 0

Solun:- Let y = cos (log x + ex)

Differentiate w.r.t. x:-

,x>0

Download PDF of Exercise 5.4 SEE Also:-

Notes of Continuity & Differentiability

Exercise 5.1

Exercise 5.2

Exercise 5.3

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