What is the derivative of f(x)=sqrt(3x+2)=(3x+2)^(1/2)?

By the power rule, the derivative of x^(n) is nx(n^1) and by the chain rule, the derivative of g(h(x)) is g'(h(x))h'(x).
Let g(x)=x^(1/2) and h(x)=3x+2 so that f(x)=g(h(x)).

Then by the power rule, g'(x)=(1/2)x^(-1/2)=1/(2x^(1/2)). Evidently, h'(x)=3.

So, by the chain rule, f'(x)=g'(h(x))h'(x)=3/(2(3x+2)^(1/2)).

Answered by Luke P. Maths tutor

4411 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find dy/dx when x+2y+3y^2= 2x^2+1


Why don't I have to put the +C after my answer for a definite integral?


How to do the product rule for differentiation


Solve the equation 3^(2x+1)=1000


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences