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How to find $bigg(frac{partial P}{partial T}bigg)_q$, given $bigg(frac{partial big(ln (P) big)}{partial...
How can I find, partial derivative of $P$ with respect to $T$ at a given $q$
$$bigg(frac{partial P}{partial T}bigg)_q$$
given that I know, partial derivative of $ln P$ with respect to $T$ at a given $q$
$$bigg(frac{partial big(ln (P) big)}{partial T}bigg)_q$$
Thanks so much.
calculus derivatives partial-derivative
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
asked Nov 20 '18 at 19:48
Karthik
83
add a comment |
How can I find, partial derivative of $P$ with respect to $T$ at a given $q$
$$bigg(frac{partial P}{partial T}bigg)_q$$
given that I know, partial derivative of $ln P$ with respect to $T$ at a given $q$
$$bigg(frac{partial big(ln (P) big)}{partial T}bigg)_q$$
Thanks so much.
calculus derivatives partial-derivative
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
asked Nov 20 '18 at 19:48
Karthik
83
Does $(f)_q$ represent the partial derivative of $f$ with respect to $q$?
– Decaf-Math
Nov 20 '18 at 19:49
no it represents partial derivative of f at constant q. $(partial f/ partial t)_q$ represents partial derivative of f with respect to t at constant q.
– Karthik
Nov 20 '18 at 19:53
add a comment |
How can I find, partial derivative of $P$ with respect to $T$ at a given $q$
$$bigg(frac{partial P}{partial T}bigg)_q$$
given that I know, partial derivative of $ln P$ with respect to $T$ at a given $q$
$$bigg(frac{partial big(ln (P) big)}{partial T}bigg)_q$$
Thanks so much.
calculus derivatives partial-derivative
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
asked Nov 20 '18 at 19:48
Karthik
83
How can I find, partial derivative of $P$ with respect to $T$ at a given $q$
$$bigg(frac{partial P}{partial T}bigg)_q$$
given that I know, partial derivative of $ln P$ with respect to $T$ at a given $q$
$$bigg(frac{partial big(ln (P) big)}{partial T}bigg)_q$$
Thanks so much.
calculus derivatives partial-derivative
calculus derivatives partial-derivative
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
asked Nov 20 '18 at 19:48
Karthik
83
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
asked Nov 20 '18 at 19:48
Karthik
83
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
edited Nov 20 '18 at 20:11
the_candyman
8,73122044
8,73122044
asked Nov 20 '18 at 19:48
Karthik
83
asked Nov 20 '18 at 19:48
Karthik
83
asked Nov 20 '18 at 19:48
Karthik
83
83
Does $(f)_q$ represent the partial derivative of $f$ with respect to $q$?
– Decaf-Math
Nov 20 '18 at 19:49
no it represents partial derivative of f at constant q. $(partial f/ partial t)_q$ represents partial derivative of f with respect to t at constant q.
– Karthik
Nov 20 '18 at 19:53
add a comment |
Does $(f)_q$ represent the partial derivative of $f$ with respect to $q$?
– Decaf-Math
Nov 20 '18 at 19:49
no it represents partial derivative of f at constant q. $(partial f/ partial t)_q$ represents partial derivative of f with respect to t at constant q.
– Karthik
Nov 20 '18 at 19:53
Does $(f)_q$ represent the partial derivative of $f$ with respect to $q$?
– Decaf-Math
Nov 20 '18 at 19:49
Does $(f)_q$ represent the partial derivative of $f$ with respect to $q$?
– Decaf-Math
Nov 20 '18 at 19:49
no it represents partial derivative of f at constant q. $(partial f/ partial t)_q$ represents partial derivative of f with respect to t at constant q.
– Karthik
Nov 20 '18 at 19:53
no it represents partial derivative of f at constant q. $(partial f/ partial t)_q$ represents partial derivative of f with respect to t at constant q.
– Karthik
Nov 20 '18 at 19:53
add a comment |
2 Answers
2
active
oldest
votes
For a smooth function $f$ you have:
$$
frac{dlog{f(x)}}{dx}=frac{f'(x)}{f(x)} Rightarrow f'(x)=f(x) frac{dlog{f(x)}}{dx}
$$
With you notation this gives:
$$
left(frac{partial P}{partial T}right)_q=P(T,q)left(frac{partial log{P}}{partial T}right)_q
$$
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
add a comment |
Notice that:
$$frac{partial big(ln (P) big)}{partial T} = frac{1}{P}frac{partial P }{partial T},$$
or equivalently:
$$frac{partial P }{partial T} = P frac{partial big(ln (P) big)}{partial T}.$$
Moreover, notice that you don't need to care about $q$ since it is assumed constant in both the expressions.
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
For a smooth function $f$ you have:
$$
frac{dlog{f(x)}}{dx}=frac{f'(x)}{f(x)} Rightarrow f'(x)=f(x) frac{dlog{f(x)}}{dx}
$$
With you notation this gives:
$$
left(frac{partial P}{partial T}right)_q=P(T,q)left(frac{partial log{P}}{partial T}right)_q
$$
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
add a comment |
For a smooth function $f$ you have:
$$
frac{dlog{f(x)}}{dx}=frac{f'(x)}{f(x)} Rightarrow f'(x)=f(x) frac{dlog{f(x)}}{dx}
$$
With you notation this gives:
$$
left(frac{partial P}{partial T}right)_q=P(T,q)left(frac{partial log{P}}{partial T}right)_q
$$
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
add a comment |
For a smooth function $f$ you have:
$$
frac{dlog{f(x)}}{dx}=frac{f'(x)}{f(x)} Rightarrow f'(x)=f(x) frac{dlog{f(x)}}{dx}
$$
With you notation this gives:
$$
left(frac{partial P}{partial T}right)_q=P(T,q)left(frac{partial log{P}}{partial T}right)_q
$$
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
For a smooth function $f$ you have:
$$
frac{dlog{f(x)}}{dx}=frac{f'(x)}{f(x)} Rightarrow f'(x)=f(x) frac{dlog{f(x)}}{dx}
$$
With you notation this gives:
$$
left(frac{partial P}{partial T}right)_q=P(T,q)left(frac{partial log{P}}{partial T}right)_q
$$
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
answered Nov 20 '18 at 20:12
Picaud Vincent
1,21838
1,21838
add a comment |
add a comment |
Notice that:
$$frac{partial big(ln (P) big)}{partial T} = frac{1}{P}frac{partial P }{partial T},$$
or equivalently:
$$frac{partial P }{partial T} = P frac{partial big(ln (P) big)}{partial T}.$$
Moreover, notice that you don't need to care about $q$ since it is assumed constant in both the expressions.
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
add a comment |
Notice that:
$$frac{partial big(ln (P) big)}{partial T} = frac{1}{P}frac{partial P }{partial T},$$
or equivalently:
$$frac{partial P }{partial T} = P frac{partial big(ln (P) big)}{partial T}.$$
Moreover, notice that you don't need to care about $q$ since it is assumed constant in both the expressions.
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
add a comment |
Notice that:
$$frac{partial big(ln (P) big)}{partial T} = frac{1}{P}frac{partial P }{partial T},$$
or equivalently:
$$frac{partial P }{partial T} = P frac{partial big(ln (P) big)}{partial T}.$$
Moreover, notice that you don't need to care about $q$ since it is assumed constant in both the expressions.
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
Notice that:
$$frac{partial big(ln (P) big)}{partial T} = frac{1}{P}frac{partial P }{partial T},$$
or equivalently:
$$frac{partial P }{partial T} = P frac{partial big(ln (P) big)}{partial T}.$$
Moreover, notice that you don't need to care about $q$ since it is assumed constant in both the expressions.
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
answered Nov 20 '18 at 20:12
the_candyman
8,73122044
8,73122044
add a comment |
add a comment |
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Does $(f)_q$ represent the partial derivative of $f$ with respect to $q$?
– Decaf-Math
Nov 20 '18 at 19:49
no it represents partial derivative of f at constant q. $(partial f/ partial t)_q$ represents partial derivative of f with respect to t at constant q.
– Karthik
Nov 20 '18 at 19:53