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).

WT
Answered by Walter T. Maths tutor

8055 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Explain why for any constant a, if y = a^x then dy/dx = a^x(ln(a))


Find the integral of a^(x) where a is a constant


Express (1 + 4 * 7^0.5)/(5 + 2 * 7^0.5) in the form m + n * 7^0.5


Find the equation of the the tangent to the curve y=x^3 - 7x + 3 at the point (1,2)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences