What method should I use to differentiate equations with an x as the power of a number. E.g. 2^x

Take the log of both sidesln(y) = ln(2^x)This can be re-written as:ln(y) = ln(2)*xTake the exponent of both sidese^ln(y) = e^(ln(2)*x)Which gives:y = e^(ln(2)*x)Since ln(2) is a constant, apply the usual method when differentiating e^nxdy/dx = ln(2)*e^(ln(2)*x)From the question y=2^x which we re-wrote as e^(ln(2)*x) so substitute in giving he final answer:dy/dx = ln(2)*2^x

BT
Answered by Billy T. Maths tutor

2822 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

On the same diagram, sketch the graphs of: y = |5x -2| and y = |2x| and hence solve the equation |5x - 2| = |2x|


If y = 4x^3 - 6x^2 + 7 work out dy/dx for this expression


A uniform ladder of mass 5 kg sits upon a smooth wall and atop a rough floor. The floor and wall are perpendicular. Draw a free body diagram for the ladder (you do not need to calculate any forces).


Express 2(x-1)/(x^2-2x-3) - 1/(x-3) as a fraction in its simplest form.


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