Given y=(1+x^3)^0.5, find dy/dx.

In order to solve this question, we need to use the chain rule when differentiating. 

The chain rule formula is dy/dx= (dy/du)*(du/dx). 

Let u=1+x3

Differentiating with respect to x gives du/dx=3x2

We now have y=u0.5

Differentiating with respect to u gives dy/du=0.5u-0.5=0.5*(1+x3)-0.5

Therefore dy/dx= (dy/du)*(du/dx)= 0.5*(1+x3)-0.5*(3x2)= 1.5x2*(1+x3)-0.5

Rebecca M. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathem...

11 months ago

Answered by Rebecca, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£30 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

Further Mathematics

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

£22 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Extended Project Qualification

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

PremiumImogen W. GCSE Chemistry tutor, GCSE Maths tutor, A Level Chemistry t...
£30 /hr

Imogen W.

Degree: Chemistry (Masters) - University College London University

Subjects offered:Maths, Chemistry


“I am very enthusiastic and patient. I want my students to be able to understand their studies so that they can enjoy them as much as I do.”

About the author

Rebecca M.

Currently unavailable: for regular students

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Psychology+ 2 more

English Literature

“About Me:I am a Warwick University maths student who has also dabbled in philosophy and mechanics modules.My Aim: A lot of the people I have helped who struggle, do so because they either lack understanding or lack passion for th...”

You may also like...

Posts by Rebecca

Given 6x+2y=4 and 5x+y=8, solve the simultaneous equations to find x and y.

Given y=(1+x^3)^0.5, find dy/dx.

Other A Level Maths questions

A curve has equation y = 4x + 1/(x^2) find dy/dx.

How do I differentiate 3^2x?

Solve the equation " 2sec^2(x) = 5tanx " for 0 < x < π

Outline the various ways that you can differentiate a function

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss