Hey! Sign in to get help with your study questionsNew here? Join for free to post

Is the derivative of a^f(x) = f'(x) (a^x)(lna) ?

Announcements Posted on
Last day to win £100 of Amazon vouchers - don't miss out! Take our quick survey to enter 24-10-2016
    • Thread Starter

    And the integral of a^f(x) = (a^f(x))/(f'(x) x lna) ?

    The integral you said isn't correct. You can't apply the reverse chain rule in that way as you get a product, so when you differentiate it you use the product rule(or quotient) and you will see that it's not right.

    hope this helps dy/dy(2^x)dx =2^xln(2) so the rule is a^x= a^xln(a)

    Proof........ dy/dx (a^x) dx....let y=a^x so ln(y)=ln(a^x) so ln(y)= xln(a) ... implicit differentiation so 1/y dy/dx =ln(a) so bringing the y up .... dy/dx = yln(a) ans as y=a^x dy/dx = a^xln(a)

    (Original post by chhhhelsie)
    And the integral of a^f(x) = (a^f(x))/(f'(x) x lna) ?
    Your derivative formula is correct, but the integral one is not, and in fact it is one of the most common misconceptions among students - specifically, the "reverse chain rule", which many students believe is true in general, in fact only applies when f(x) is linear (of the form ax+b). Thus for example the integral of e^(x^2), letting f(x)=x^2 and a=e in other words, is not e^(x^2)/2x - in fact, this function e^(x^2) is impossible to integrate, although the proof of this result is beyond A-Level.

    Integral (a^xln(a)) dx = a^x as its the thing you differentiated so go back
Write a reply…


Submit reply


Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: June 20, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Would you rather find
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read here first


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.