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shadow0191
@shadow0191
July 2022
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Помогите 2 производные срочно!!![tex]y=ln^3(1+e^-^5^x)
y=ln \sqrt{1+e ^{2x}+e^4^x } [/tex]
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sharadi
Verified answer
1) y' = -15 ln²(1 + e⁻⁵ˣ) * 1/(1 + e⁻⁵ˣ) * e⁻⁵ˣ = -15e ⁻⁵ˣln²(1 + e⁻⁵ˣ)/(1 + e⁻⁵ˣ)
2) y'= 1/√(1 + e²ˣ + e⁴ˣ) * (√(1 + e²ˣ + e⁴ˣ) )'=
= 1/√(1 + e²ˣ + e⁴ˣ) * 1/2√(1 + e²ˣ + e⁴ˣ) *(1 + e²ˣ + e⁴ˣ)' =
= 1/2(1 + e²ˣ + e⁴ˣ) * (2e²ˣ + 4e⁴ˣ) = (e²ˣ + 2e⁴ˣ)/ (1 + e²ˣ + e⁴ˣ)
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Verified answer
1) y' = -15 ln²(1 + e⁻⁵ˣ) * 1/(1 + e⁻⁵ˣ) * e⁻⁵ˣ = -15e ⁻⁵ˣln²(1 + e⁻⁵ˣ)/(1 + e⁻⁵ˣ)2) y'= 1/√(1 + e²ˣ + e⁴ˣ) * (√(1 + e²ˣ + e⁴ˣ) )'=
= 1/√(1 + e²ˣ + e⁴ˣ) * 1/2√(1 + e²ˣ + e⁴ˣ) *(1 + e²ˣ + e⁴ˣ)' =
= 1/2(1 + e²ˣ + e⁴ˣ) * (2e²ˣ + 4e⁴ˣ) = (e²ˣ + 2e⁴ˣ)/ (1 + e²ˣ + e⁴ˣ)