MYTUTOR SUBJECT ANSWERS

455 views

How do you take the derivative of a^x ?

There are two ways you can take the derivative of a^x.

1) 

Let y = a^x    now we're trying to find dy/dx

2)

ln(y) = xln(a)    take logs of both sides and use log rules

3)

(dy/dx)*(1/y) = ln(a)   take the derivative of both sides using the chain rule                                           on the left hand side.

4)

dy/dx = ln(a)*y              multiply both sides by y

5)

dy/dx =  ln(a) *a^x        realise y= a^x and replace it

Now we're done!

Alternatively we could realise that any exponent can be written as e to the power of something with a log in it.

So

1)

y = a^x = (e^ln(a))^x    just rewritting 'a'

2)

y = e^xln(a)                multiplying exponent rule

3)

dy/dx = ln(a)*e^xln(a)   take the derivative of both sides using the chain                                                   rule for the right hand side

4)

dy/dx  = ln(a)*a^x                         substitute back to get desired result

Expired account  . A Level Maths tutor, GCSE Maths tutor, A Level Fur...

1 year ago

Answered by Expired account, who tutored A Level Maths with MyTutor


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

297 SUBJECT SPECIALISTS

£20 /hr

Sarah H.

Degree: Mathematics (Bachelors) - Edinburgh University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Biology

“I am studying mathematics at the University of Edinburgh. I've always been enthusiastic about maths and the sciences in general (particularly biology) and I hope I can pass on my passion for the subjects. During the sessions we will f...”

MyTutor guarantee

£20 /hr

Elizabeth P.

Degree: Geophysics (Bachelors) - Durham University

Subjects offered:Maths, -Personal Statements-

Maths
-Personal Statements-

“Hey there! My name is Libby and I’m currently in my final year studying Geophysics at Durham university. I love to get other people as excited about maths and science as I am and have done so by tutoring at school, being involved outr...”

MyTutor guarantee

£20 /hr

George T.

Degree: Architecture (Bachelors) - Sheffield University

Subjects offered:Maths

Maths

“I'm an architecture student. I want to support this higher education by tutoring others. I believe in supportive sessions that develop independent study skills.”

MyTutor guarantee

About the author

Expired account  . A Level Maths tutor, GCSE Maths tutor, A Level Fur...
£22 /hr

Expired account .

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Further Mathematics
Chemistry

“Hi, my name's Sam and I'm a mathematics (and physics) student at Durham. I know for some people the most important thing is just to get through their exams; I can andwill help you with this. I can't stress enough, however, how much e...”

You may also like...

Posts by Expired account

How do you take the derivative of a^x ?

How does integration work?

Some videos I've made

What is the best way to prove trig identities?

Other A Level Maths questions

If y = (4x^2)ln(x) then find the second derivative of the function with respect to x when x = e^2 (taken from a C3 past paper)

The volume of liquid in a container is given by v=(3h^2+4)^(3/2)-8, find dV/dh when h = 0.6

What is a derivative?

what is implicit differentiation and how is it achieved?

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