Can the natural logarithm, $ln$, have an exponent?
$begingroup$
$$f(x)=ln^3(x^2+tan(3x))$$
This is a question from a past final exam. I need to derive this function and I have one simple question. Is it possible for that natural log to have its own exponent. How would I even go about deriving this problem seeing as how $frac{d}{dx}(ln(x)) = frac{1}{x}$ ?
derivatives logarithms exponential-function
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
$endgroup$
add a comment |
$begingroup$
$$f(x)=ln^3(x^2+tan(3x))$$
This is a question from a past final exam. I need to derive this function and I have one simple question. Is it possible for that natural log to have its own exponent. How would I even go about deriving this problem seeing as how $frac{d}{dx}(ln(x)) = frac{1}{x}$ ?
derivatives logarithms exponential-function
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
$endgroup$
$begingroup$
Yes it's possible, you just use the chain rule several times.
$endgroup$
– DMcMor
Apr 29 '17 at 1:52
add a comment |
$begingroup$
$$f(x)=ln^3(x^2+tan(3x))$$
This is a question from a past final exam. I need to derive this function and I have one simple question. Is it possible for that natural log to have its own exponent. How would I even go about deriving this problem seeing as how $frac{d}{dx}(ln(x)) = frac{1}{x}$ ?
derivatives logarithms exponential-function
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
$endgroup$
$$f(x)=ln^3(x^2+tan(3x))$$
This is a question from a past final exam. I need to derive this function and I have one simple question. Is it possible for that natural log to have its own exponent. How would I even go about deriving this problem seeing as how $frac{d}{dx}(ln(x)) = frac{1}{x}$ ?
derivatives logarithms exponential-function
derivatives logarithms exponential-function
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
edited Apr 29 '17 at 8:30
projectilemotion
11.4k62141
11.4k62141
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
asked Apr 29 '17 at 1:51
M.BucciacchioM.Bucciacchio
476
476
$begingroup$
Yes it's possible, you just use the chain rule several times.
$endgroup$
– DMcMor
Apr 29 '17 at 1:52
add a comment |
$begingroup$
Yes it's possible, you just use the chain rule several times.
$endgroup$
– DMcMor
Apr 29 '17 at 1:52
$begingroup$
Yes it's possible, you just use the chain rule several times.
$endgroup$
– DMcMor
Apr 29 '17 at 1:52
$begingroup$
Yes it's possible, you just use the chain rule several times.
$endgroup$
– DMcMor
Apr 29 '17 at 1:52
add a comment |
1 Answer
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$begingroup$
Actually, this can be rewritten as $(ln(x^2+tan(3x)))^3$ just like how trig functions like $sin^2(x)$ are analogous to saying $(sin(x))^2$
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
$endgroup$
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
add a comment |
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
Actually, this can be rewritten as $(ln(x^2+tan(3x)))^3$ just like how trig functions like $sin^2(x)$ are analogous to saying $(sin(x))^2$
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
$endgroup$
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
add a comment |
$begingroup$
Actually, this can be rewritten as $(ln(x^2+tan(3x)))^3$ just like how trig functions like $sin^2(x)$ are analogous to saying $(sin(x))^2$
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
$endgroup$
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
add a comment |
$begingroup$
Actually, this can be rewritten as $(ln(x^2+tan(3x)))^3$ just like how trig functions like $sin^2(x)$ are analogous to saying $(sin(x))^2$
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
$endgroup$
Actually, this can be rewritten as $(ln(x^2+tan(3x)))^3$ just like how trig functions like $sin^2(x)$ are analogous to saying $(sin(x))^2$
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
edited Jan 7 at 10:15
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
answered Apr 29 '17 at 1:53
rb612rb612
1,8481923
1,8481923
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
add a comment |
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
$begingroup$
oh gosh, I thought it might be something like that. It's confusing since not once has my teacher or the textbook shown it like that .
$endgroup$
– M.Bucciacchio
Apr 29 '17 at 1:55
add a comment |
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$begingroup$
Yes it's possible, you just use the chain rule several times.
$endgroup$
– DMcMor
Apr 29 '17 at 1:52