If y = 2(x^2+1)^3, what is dy/dx?

Since the equation for y is a composite function (applying one function to another function) we need to use the chain rule to answer this question. Firstly let u = x^2+1 . This allows us to write y = 2u^3. Differentiating y with respect to u gives us: dy/du = 6u^2. Next we differentiate our equation for u with respect to x, which gives us: du/dx = 2x Finally we use these two equations to obtain dy/dx by using the following formula: dy/dx = (dy/du)(du/dx) = (6u^2)(2x) = (6(x^2+1)^2)*(2x) = 12x(x^2+1)^2 Hence we have obtained dy/dx in terms of x and y.

GC
Answered by Gemma C. Maths tutor

3914 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate and factorise y = x^2(3x + 1)


find dy/dx when y=x^3 + sin2x


A curve is defined by the parametric equations x = 3^(-t) + 1, y = 2 x 2^(t). Show that dy\dx = -2 x 3^(2t).


Let f(x)= x^3 -9x^2 -81x + 12. Calculate f'(x) and f''(x). Use f'(x) to calculate the x-values of the stationary points of this function.


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