MYTUTOR SUBJECT ANSWERS

537 views

If y = (4x^2)ln(x) then find the second derivative of the function with respect to x when x = e^2 (taken from a C3 past paper)

The first thing to recognise is that this function is a product of two functions: namely, 4x^2 and ln(x), thus we must employ the product rule in order to find the solution. As you may recall, the product rule states that when you have a function f(x) = uv, the differential f'(x) = udv + vdu, thus:

we differentiate once, finding that dy/dx = (4x^2)/x + 8xln(x) and simplify to get the expression 4x + 8xln(x)

then differentiate a second time, remembering to once again employ the product rule for the second term in the equation:

d^2y/dx^2 = 4 + (8 + 8ln(x))

now substitute the value of x = e^2 into the equation:

thus d^2y/dx^2 = 12 + 8ln(e^2)

now as we know that the natural logarithm "ln" is the inverse of the exponential function "e", this becomes:

d^2y/dx^2 = 12 + 8(2)

= 28.

Caspar S. Uni Admissions Test .MAT. tutor, Mentoring -Personal Statem...

1 year ago

Answered by Caspar, an A Level Maths tutor with MyTutor


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

296 SUBJECT SPECIALISTS

£20 /hr

Kirill M.

Degree: Physics (Masters) - Oxford, St Catherine's College University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.PAT.

“Me Hi, I'm Kirill, I'm a 3rd year physicist at Oxford. Whether you are looking for exam preparation or for a better understanding of the material that you are covering in your studies of Maths or Physics, I can help you reach your goa...”

£20 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best! ”

MyTutor guarantee

£22 /hr

Kyle W.

Degree: Computer Science (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“About me Hi my name is Kyle! I'm currently in my second year studying Computer Science at the University of Bristol. I've always had a passion for mathematics and studying computer science has gave me an appreciation for just how many...”

About the author

Caspar S.

Currently unavailable: for regular students

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Physics+ 5 more

Maths
Physics
Further Mathematics
English Literature
.MAT.
-Personal Statements-

“Me:I study MORSE at Warwick University (unfortunately no, it's not morse code) and hope that my expertise in both teaching and learning maths (as well as a couple of other things) will translate into a great learning experience for y...”

You may also like...

Other A Level Maths questions

How do you find an angle in a right-angled triangle when you are given two of its side's lengths?

When would you apply the product rule in differentiation and how do you do this?

Find the solution(s) of 3(x^2)-6x+2=0

Integration

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

mtw:mercury1:status:ok