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

7860 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Curve C has equation x^2 - 3xy - 4y^2 + 64 = 0. a) find dy/dx in terms of x and y. b) find coordinates where dy/dx=0.


Find the gradient of the curve y = sin(2x) + 3 at the point where x = pi


Find the stationary points of y = 4(x^2 - 4)^3


A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.


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