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122/1000, derivative of f^g, implicit differentiation

• bprp calculus b… 25일 전 2026.09.06 16:00 인기
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이전글#maths2026.09.04
다음글Subtração de números inteiros.2026.09.07
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@militantpacifi… 　25일 전

Side note: f and f’ do NOT cancel.

2026-09-07 06:56

[ytcid:UgxpeH_A9hr8r4MNB6x4AaABAg] Side note: f and f’ do NOT cancel.



@anonymouschees… 　25일 전

f^g = e^glnf
(f^g)’ = e^glnf * (g’lnf + gf’/f)
d/dx (f^g) = f^g * (g’lnf + gf’/f)

2026-09-07 06:35

[ytcid:Ugzl7DR6Rih7P2iYhmF4AaABAg] f^g = e^glnf (f^g)’ = e^glnf * (g’lnf + gf’/f) d/dx (f^g) = f^g * (g’lnf + gf’/f)



@Nore2554 　25일 전

f^g  =  e^ln(f^g)  =  e^(g•ln(f)

Apply chain rule

d/dx(e^(g•ln(f)))  =  e^(g•ln(f))•d/dx(g•ln(f))

Revert the first part back to "f^g" and apply product rule

(f^g)•d/dx(g•ln(f))  =  (f^g)•(g'•ln(f)+g•(f'/f))

2026-09-06 21:36

[ytcid:UgyF839lej2DDtfrpPF4AaABAg] f^g = e^ln(f^g) = e^(g•ln(f) Apply chain rule d/dx(e^(g•ln(f))) = e^(g•ln(f))•d/dx(g•ln(f)) Revert the first part back to "f^g" and apply product rule (f^g)•d/dx(g•ln(f)) = (f^g)•(g'•ln(f)+g•(f'/f))



@khaleddamha312… 　25일 전

????????

2026-09-06 17:51

[ytcid:UgzYk8ovnny2TsY1xJB4AaABAg] ????????



@ImadAjjaj 　25일 전

122?

2026-09-06 17:08

[ytcid:Ugy9WujnOzk5E89OcdR4AaABAg] 122?



@vikramrawat526… 　25일 전

Day 122

2026-09-06 16:25

[ytcid:UgxmDbcTOMK_tjFVCG14AaABAg] Day 122



@hail-hydra-911 　25일 전

This is basically the x^x situation! Why has no one ever used the product rule like you just did by pretending the other part be constant before?

2026-09-06 16:11

[ytcid:Ugxk1hV_OCXNyYRICMV4AaABAg] This is basically the x^x situation! Why has no one ever used the product rule like you just did by pretending the other part be constant before?



@terrylewis5786 　24일 전

Nice

2026-09-07 13:03

[ytcid:UgzLJJIMBXzUL4Jj0st4AaABAg] Nice



@NonameBozo88 　23일 전

There is no justification for the first step , assume g is constant, based on what , and then it is not constant.
Then having matching results doesn't justify correctness of the first one only that it matches the correct answer either by fluck or no proper reasoning provided

2026-09-08 13:07

[ytcid:UgzvhrBAoMITc2SK_Gt4AaABAg] There is no justification for the first step , assume g is constant, based on what , and then it is not constant. Then having matching results doesn't justify correctness of the first one only that it matches the correct answer either by fluck or no proper reasoning provided