How do we differentiate y=a^x when 'a' is an non zero real number

Firstly we must change it into a form we can deal with. To do this we take the natural log (ln) of both sides.ln(y)=ln(ax) ln(y)=x(ln(a))    using our rules of logsFrom here we differentiate. The differential of ln(f(x)) is [(d/dx)f(x)]/f(x)(dy/dx)/y=ln(a)      differentiating from above rule and ln(a) is just a constant so d/dx xln(a)= ln(a)dy/dx=yln(a)    times both sides by ydy/dx=(ax)(ln(a)) subbing in y=ato get dy/dx in terms of x

MJ
Answered by Marcus J. Maths tutor

8154 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve x(5(3^0.5)+4(12^0.5))=(48^0.5) to the simplest form. (4 Marks)


Find the exact gradient of the curve y = ln(1-cos 2x) at the point with x-coordinate π/6.


f(x) = (4x + 1)/(x - 2). Find f'(x)


What is the coefficient of x^4 in the expansion of (x+3)^7


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:

© 2026 by IXL Learning