Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$\[\]$y=(x^{2}+5)^{3},x=1,dx=0.1$

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

1 Answer

Comment
A)
Toolbox:
  • Let $y=f(x)$ be a differentiable function then the quantities $dx$ and $dy$ are called differentials.The differential $dx$ is an independent variable.
  • The differential $dy$ is then defined by $dy=f'(x)dx(dx \approx \Delta x)$
  • Also $f(x+\Delta x)-f(x)=\Delta y =dy $ from which $f(x+\Delta x) $can be evaluated
Step 1:
$y=(x^2+5)^3$
$dy=3(x^2+5)^2-2xdx$
$\quad=6x(x^2+5)^2dx$
Step 2:
When $x=1,dx=0.05$
$dy= 6(6)^2(0.05)$
$\quad=216 (0.05)$
$\quad=10.8$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...