MYTUTOR SUBJECT ANSWERS

3450 views

How do you differentiate 2 to the power x?

let y=2x                 {take natural logs of both sides}

ln y = ln(2x)          {use rules of logs to change right hand side}

lny = xln2              {differentiate implicitly}

1/y dy/dx = ln2    {make dy/dx the subject}

dy/ dx       = y ln2  {write y in terms of x)

dy/dx = 2x . ln2

Therefore derivative of 2 to the power of x is 2x . ln2

 

This can be generalised as the derivative of a to the power of x (where a is a constant, a>0)  is  ax lna

Jack R. GCSE Maths tutor, A Level Maths tutor

2 years ago

Answered by Jack, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

257 SUBJECT SPECIALISTS

PremiumRyan G. GCSE Maths tutor, GCSE Physics tutor, GCSE Computing tutor, A...
£24 /hr

Ryan G.

Degree: Electrical Engineering with Renewable Energy (Masters) - Edinburgh University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Computing
-Personal Statements-

“ I will offer a wide range of ways to learn so you can find a way that best suits you!”

£30 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£22 /hr

Ben T.

Degree: Engineering (Bachelors) - Cambridge University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
French
Chemistry
-Personal Statements-
-Oxbridge Preparation-

“Hi there! I’m your friendly neighbourhood Cambridge grad, brimming with tricks and enthusiasm for Maths, Sciences and French. To learn more, view my profile...”

About the author

£20 /hr

Jack R.

Degree: mathematics (Bachelors) - Sheffield University

Subjects offered:Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Differentiate y=sin(x)/5x^3 with respect to x

Find the solutions to z^2 = i

Differentiate y=x/sin(x)

How do I integrate log(x) or ln(x)?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok