MYTUTOR SUBJECT ANSWERS

726 views

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

y = e2x(x2+1)5/2

The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation:

y = uv

where u = e2x and v = (x2+1)5/2. We now differentiate u and v separately with respect to x.

Here, remember that df(g(x))/dx is equal to df/dg times dg/dx. So,

du/dx = 2e2x and dv/dx = 5/2 (x2+1)3/2 2x = 5x(x2+1)3/2

Using the chain rule,

dy/dx = u dv/dx + v du/dx

= e2x 5x(x2+1)3/2 + 2e2x (x2+1)5/2.

Now, when x=0, the first term disappears, since it's multipled by x. exp(0) is equal to 1, as is 15/2, so the second term reduces to 2 times 1. The answer is therefore 2.

Adam S. A Level Further Mathematics  tutor, A Level Maths tutor, A Le...

2 years ago

Answered by Adam, an A Level Maths tutor with MyTutor


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

307 SUBJECT SPECIALISTS

£24 /hr

Ayusha A.

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

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
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

Georgia S.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Design & Technology

“Hi, I'm Georgia. I'm a Maths student with a passion for learning and with enough enthusiasm to inspire anyone to love Maths too!”

Katherine H. A Level Further Mathematics  tutor, GCSE Further Mathema...
£30 /hr

Katherine H.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Geography+ 1 more

Maths
Geography
Further Mathematics

“I am a first-year undergraduate for a masters degree in Mathematics at the University of Bath. I achieved full UMS marks in Mathematics (600/600), Further Mathematics (600/600), Geography and Psychology A Levels. I have tutored on num...”

About the author

Adam S.

Currently unavailable: for regular students

Degree: Artificial Intelligence (Masters) - York University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I love maths and physics. I loved them as a child, I loved them at university and I even loved them at school. I hope that during my tutorials you will grow to love these subjects too. About me I graduated from the University of York...”

You may also like...

Posts by Adam

Given that abc = -37 + 36i; b = -2 + 3i; c = 1 + 2i, what is a?

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

Other A Level Maths questions

Differentiate with respect to X: x^2 + 2y^2+ 2xy = 2

How do I find the cartesian equation for a curve written in parametric form?

What is the product rule and when do you use it?

The polynomial x^3 - 2*x + a, where x is a constant is denoted by p(x). It is given that x+2 is a factor of p(x). Find a

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