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Chain rule

OhMyMarkov

Member
Mar 5, 2012
83
Hello everyone, I remember this from single-variable calculus: if f(x) = 2x, then df = 2dx, right?

What if $f(r, \theta) = r\cos \theta$, how can I express $\partial f$ in terms of $r$ and $\theta$.?

Thanks!
 
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chisigma

Well-known member
Feb 13, 2012
1,704
Hello everyone, I remember this from single-variable calculus: if f(x) = 2x, then df = 2dx, right?<br><br>What if $f(r, \theta) = r\cos \theta$, how can I express $\partial f$ in terms of $r$ and $\theta$.?<br><br>Thanks!
In Your case $f(r, \theta)$ is function of two variables, $r$ and $\theta$, so that is...

$\displaystyle df= f_{r}\ dr + f_{\theta}\ d \theta$ (1)

... where $f_{r}$ and $f_{\theta}$ are the partial derivatives of $f(*,*)$ respect to $r$ and $\theta$...

Kind regards

$\chi$ $\sigma$
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
Notice that you do NOT use the "curly d" here. It is df, not $\partial f$.