MYTUTOR SUBJECT ANSWERS

490 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...

1 year ago

Answered by Adam, an A Level Maths tutor with MyTutor


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

257 SUBJECT SPECIALISTS

£22 /hr

Jonathan D.

Degree: Natural Sciences (Physical) (Bachelors) - Cambridge University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“2nd year Natural Sciences student at Cambridge - massively passionate about all things Maths and Science, and I would love to be able to help!”

£20 /hr

Eleanor S.

Degree: Physics (Masters) - Durham University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
French

“About Me: Hi, I'm Elle! Science, maths and languages have been my favourite subjects from a young age and studying them in further detail only made me love them more. I am soon to go into my second year of a physics degree at Durham ...”

£20 /hr

Jamie S.

Degree: Economics and Management (Bachelors) - Bristol University

Subjects offered: Maths, Economics

Maths
Economics

“I am a final year student at the University of Bristol, studying Economics and Management and am currently on track to achieve a 1st. I achieved an A* in Economics and an A in Maths A-levels as well as an A* at maths GCSE so would be ...”

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

How do I know when to differentiate using the chain rule? And how do I do this?

How should I aproach a connected rates of change question.

Differentiate y = (6x-13)^3 with respect to x

The quadratic equation 2x^2 + 8x + 1 = 0 has roots x1 and x2. Write down the value of x1+x2 and x1*x2 and find the value of x1^2 + x2^2

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok