Answers>Maths>IB>Article

How do I find the derivative of 2^x?

To find the derivative of any number to the power "x", such as 2x, 5x, or even 4.13x, we first consider the general form ax. We need to be a little creative here. We know that any variable y can be rewritten as elny.  If we then say that y = ax then we can say that y= elnax. Note that this is because ln(a)x=xlna. So that means y = ax = elna * x. Now we want to find the derivative of ax, or (elna * x )', which is lna ex(lna). This is because lna is a definite number, and so we derivate this the same way we would e3x (which would be 3e3x). Now, if the derivative equals lna ex(lna) we see that actually, ex(lna) is equal to y, so we can rewrite this further as lnay. Since y = ax we can simplify this finally to lnaax. That means that the derivative of ax is axlna. This is the general form and should be remembered. So, (2x)'= 2xln2. 

KS
Answered by Katerina S. Maths tutor

40012 Views

See similar Maths IB tutors

Related Maths IB answers

All answers ▸

How should I approach a proof by induction question?


Differentiation from first principles


Given h(x) = 9^x + 9 and g(x) = 10*3^x, find {x | h(x) < g(x)}.


Given two functions f and g where f(x)=3x-5 and g(x)=x-2. Find: a) the inverse f^-1(x), b) given g^-1(x)=x+2, find (g^-1 o f)(x), c) given also that (f^-1 o g)(x)=(x+3)/3, solve (f^-1 o g)(x)=(g^-1 o f)(x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences