Ni hesabu gani formula zake zilikupa shida?

conductor

JF-Expert Member
May 29, 2013
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Ni formula ipi hukuwahi kutana nayo kwenye haratakati zako za shule mpaka Chuo?.je ipi hujui matumiz yake?in real life.?
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Hapo kwenye x substitute 8e^-2 -4, ni hicho tu ndicho nilichosahau kuweka ili kupata jibu sahihi., lakini hilo ni jibu unsimplified.

Shida watu tumecrame d/dx e^x=e^X bila kujua imekujaje.


X=8e^-2t-4
(X+4)=8e^-2t rearranging

Taking Ln on both sides

Ln(x+4)=Ln8e^-2t=Ln8-2t Lne

d/dt[(X+4)=Ln8e-2t Lne]

1/(x+4)dx=0-2dt
dx/dt= -2(x+4)

Now substitute x=8e^-2t-4 into -2(x+4) for dx/dt., this becomes

dx/dt=-2(8e^-2t-4+4)= -16e^-2t.


Hiyo ndiyo first principle ambayo mtu anatakiwa aijue kabla ya kujua d/dx Ne^ax=Nae^ax.
 
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The power doesn't change when you differentiate e²ᵗ.
Since the derivative of e^x is e^x
The derivative of 8e⁻²ᵗ is -2(8)e⁻²ᵗ

dx/dt = -16e⁻²ᵗ

Trick is to stick dx/dt ignore y = 2e²ᵗ + 4.


Upo sahihi, jibu langu ni incomplete kwani nilitumia the first principle ku solve na nikasahau kwenye X ku substitute equation yenyewe x=(8e^-2t-4).
 

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