Find dy/dx of y = a^x

To differentiate a function of the form y=a^x you need to use a neat little trick to rewrite a^x in the form of something you already know how to differentiate. Using the fact that e^ln(x) is equal to x, y = a^x can be written as e^(ln(a)^x) Using log rules ln(a)^x can be written as xlna so now y can now be expressed as y = e^(xlna) This can now be differentiated using the chain rule. Also recall that the differential of e^x is e^x. Using these two ideas: where y=e^(xlna) dy/dx = (lna)e^(xlna) now we can substitute in our initial expression y=a^x therefore dy/dx = (a^x)lna. using this method, you can differentiate any function of the same form. for example where y=2^x we can see that a=2 so dy/dx = 2^xln2

TD
Answered by Tutor33284 D. Maths tutor

23274 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the intergal of 2x^5 -1/(4x^3) -5 giving each term in its simplest form.


A block of mass 5kg is on a rough slope inclined at an angle of 30 degrees to the horizontal, it is at the point of sliding down the slope. Calculate the coefficient of friction between the block and the slope.


A function f is defined by f(x) = x^3 - 3x^2 + 1. i) Write down f'(x). ii) Hence find the co-ordinates of the stationary points of the curve y=f(x).


differentiate- X^3- 2X^2+3


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning