]]>
LearnNext
Get a free home demo of LearnNext

Available for CBSE, ICSE and State Board syllabus.
Call our LearnNext Expert on 1800 419 1234 (tollfree)
OR submit details below for a call back

clear

Derivatives of Exponential and Logarithmic Functions

4,504 Views
Have a doubt? Clear it now.
live_help Have a doubt, Ask our Expert Ask Now
format_list_bulleted Take this Lesson Test Start Test

Derivatives of Exponential and Logarithmic Functions - Lesson Summary

The derivative of ex  w.r.t. x = d/dx (ex) = ex

The derivative of log x w.r.t. x = d/dx (log x) = 1/x

The derivative of a function that is the power of another function i.e

y = f(x) = [u(x)]v(x)

Taking logarithm to base e, we get

log y = log[u(x)]v(x)

⇒ log y = v(x) log u(x)

Differentiating both the sided w.r.t. x, we get

d/dx(log y) = d/dx[v(x) log u(x)]

⇒ 1/y dy/dx = d/dx[v(x) log u(x)]

⇒ 1/y dy/dx = v(x).1/u(x).u'(x) + v'(x).log u(x)

∴ dy/dx = y[v(x).1/u(x).u'(x) + v'(x).log u(x)]

In this case, the logarithmic differentiation method is applicable only if functions f(x) and u(x) are positive.

Logarithmic differentiation is a process by which a complex function can be differentiated by taking logarithm to base e of the function and then differentiating both the sides.

Comments(0)

Feel the LearnNext Experience on App

Download app, watch sample animated video lessons and get a free trial.

Desktop Download Now
Tablet
Mobile
Try LearnNext at home

Get a free home demo. Book an appointment now!

GET DEMO AT HOME