menu

arrow_back Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if \[ y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \]

by Platinum
(103,030 points)
in Mathematics
4 views
Determine \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) if
\[
y=\left(x^{2}+\frac{1}{x^{2}}\right)^{2}
\]

1 Answer

Best answer
0 like 0 dislike
 
Best answer
Multiply out and simplify
We need to get \(y\) into a form that we know how to differentiate.
\[
\begin{aligned}
y &=\left(x^{2}+\frac{1}{x^{2}}\right)^{2} \\
&=x^{4}+2 \frac{x^{2}}{x^{2}}+\frac{1}{x^{4}} \\
&=x^{4}+2+\frac{1}{x^{4}} \\
&=x^{4}+2+x^{-4}
\end{aligned}
\]
Differentiate the simplified expression
\[
\begin{aligned}
y &=x^{4}+2+x^{-4} \\
\therefore \frac{\mathrm{d} y}{\mathrm{~d} x} &=4 x^{3}-4 x^{-5}
\end{aligned}
\]
by Platinum
(103,030 points)

Related questions


Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve  $\cos x \frac{d y}{d x}=1+y \sin x$ (where $\left.-\frac{\pi}{2}<x<\frac{\pi}{2}\right)$ explicitly.
0 answers 5 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Evaluate: \(\int_{1}^{3}\left(\frac{x-1}{(x+1)^{2}}\right) \mathrm{d} x\)
1 answer 45 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
$\int\left(\frac{1}{x^{2}}+\frac{6}{x^{3}}\right) d x$
1 answer 53 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Show that $\frac{d}{d x}\left(\sin ^{-1} x\right)=\frac{1}{\sqrt{1-x^{2}}}$
1 answer 51 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Determine the integral $\int \left(x^{\frac{1}{3}}+\dfrac{1}{x^{\frac{3}{2}}}\right)dx$
1 answer 115 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the general solution for $x>3$. For $x>3$, we have $$ \frac{d y_{2}}{d x}+2 y_{2}=-2, \quad y_{2}(3)=y_{1}(3) $$
1 answer 36 views
close

Join MathsGee Homework Help Q&A where you get study support for success from our verified experts. We provide answers to subject-specific educational questions for improved outcomes.


On the MathsGee Homework Help Q&A learning community, you can:


  1. Ask questions
  2. Answer questions
  3. Comment on Answers
  4. Vote on Questions and Answers
  5. Donate to your favourite users
  6. Create/Take Live Video Lessons

Posting on the MathsGee Homework Help Q&A learning community


  1. Remember the human
  2. Behave like you would in real life
  3. Look for the original source of content
  4. Search for duplicates before posting
  5. Read the community's rules

MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Management Leadership | MathsGee ZOOM | eBook | H5P