Differentiate y = √(1 + 3x²) with respect to x

To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In this example, if we let u = 1 + 3x², then we get y = √(u), which means when we differentiate with respect to u, dy/du = 1/(2√(u)). u = 1 + 3x² which means du/dx = 6x, so dy/dx = 6x/(2√(u)), or 3x/√(1 + 3x²). (This can also be expressed as 3x(1 + 3x²)^-0.5).

Answered by Walter T. Maths tutor

7825 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can you integrate ln(x) with respect to x?


You deposit 500 pounds at time t=0. At t=5 years, you have 800 pounds. The amount of money you have in the bank can be modeled as V(t)=A*(1+r)^t, where r is the interest rate. Find A and the interest rate r. After how many years will you have 1200 pounds.


Find the turning point of the line y = x^2 + 2x -1


Solve the differential equation: (dy/dx) = 6xy^2


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