Waste less time on Facebook — follow Brilliant.
×

Help: understanding partial derivative

We are given \(x = r\cos \theta\) and \(y = r\sin \theta\). Find partial derivative of 'r' w.r.t 'x'.
I tried solving this way
\(r = x\sec \theta\).
\(\frac{dr}{dx}\) = \(\sec \theta\). [ I have used the symbol 'd' for partial derivative].
Also,squaring and adding both equations in question we get,
\(r^2 = x^2 + y^2\).
\(2r\frac{dr}{dx} = 2x\).
\(\frac{dr}{dx} = \frac{x}{r}\).
\(\frac{dr}{dx} = \frac{r\cos \theta}{r}\) [As given, \(x=r\cos \theta\)].
= \(\cos \theta\).
I got two different answers I am confused where am i wrong?

Note by Sonveer Yadav
11 months, 2 weeks ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Do you know what a partial derivative is?

Did you apply the product rule correctly?

Hint: Does \( \theta \) depend on \(x\)?

Calvin Lin Staff - 11 months, 1 week ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...