differentiate x^3(1+x)^5 with respect for x

First we have to use the product rule, remember that if we have h(x)=f(x)g(x) then h'(x)=f'(x)g(x)+f(x)g'(x).

So h'(x) = x^3D[(x+1)^5]+(x+1)^5D[x^3]

Completing the unfinished derivatives,

h'(x) = x^3[5(x+1)^4]+(x+1)^5[3x^2]

Simplifies to.

h'(x) = 5x^3(x+1)^4+3x^2(x+1)^5

remember that we do the (x+1)^5 in the standard way. 

Robert L. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...

7 months ago

Answered by Robert, a GCSE Maths tutor with MyTutor

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


Hannah L. GCSE Art tutor, A Level Art tutor, GCSE Maths tutor, 13 plu...
View profile
£18 /hr

Hannah L.

Degree: Petroleum Engineering (Bachelors) - Manchester University

Subjects offered: Maths, Science+ 1 more


“I am a Petroleum Engineering student at the University of Manchester. I am extremelly passionate about mathematics and physics, but can also offer study help in areas such as other sciences, art and geology.  I am a very enthusiastic,...”

MyTutor guarantee

Riccardo P. A Level Italian tutor, A Level Latin tutor, A Level Maths...
View profile
£18 /hr

Riccardo P.

Degree: physics (Bachelors) - Imperial College London University

Subjects offered: Maths, Physics+ 1 more


“Hi, I'm Riccardo, a physics fresher at London's Imperial College from Milan. As you can imagine I really like physics and maths, but that doesn't mean I'll spend all my time studying! I'm an active guy who loves sports (boxing, diving ...”

MyTutor guarantee

PremiumElicia T.
View profile
£22 /hr

Elicia T.

Degree: Security and Justice (Masters) - Leeds University

Subjects offered: Maths, Sociology+ 3 more


“My name is Elicia and I am currently studying a Law Masters in Security and Justice at the University of Leeds. I recently graduated from the same university with aLLB Law degree. My ambition is to complete a PhD in law and become a u...”

MyTutor guarantee

About the author

Robert L. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...
View profile

Robert L.

Currently unavailable: for regular students

Degree: Natural Sciences (Masters) - Durham University

Subjects offered: Maths, Physics+ 1 more


“Mathematically minded Durham Natural Scientist with fantastic A-Level results I could pass on to you! Full marks in 3/4 Geography exams, FP3 and M2.Super experienced tutor, helped students independently whilst in sixth form, voluteer...”

You may also like...

Posts by Robert

differentiate x^3(1+x)^5 with respect for x

Evaluate how plate tectonics theory helps our understanding of the distribution of seismic and volcanic events.

How would you use electron diffraction to estimate nuclear diameter

solve z^4=2(1+isqrt(3)) giving roots in form r(cos(theta)+isin(theta))

Other GCSE Maths questions

What can I say about the roots of a quadratic equation without actually calculating them?

What is the difference between a parametric equation and a general equation?

How do I solve a quadratic equation?

How do I find the equation of a line connecting points a(p,q) and b(r,s)?

View GCSE Maths tutors


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