tex]...

July 2022 1 7 Report

Найдите производные сложных функций:
1) [tex]1) y=ln^{2} (5^{x+1} +e^{x}).\\ 2) y=-x^{e}+tgln(8x^{2}+5x).\\ 3) y=( \frac{1+x^{6} }{x^{2}-6 })^{3}[/tex]

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igorShap

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$1)(ln^{2} (5^{x+1} +e^{x}))'=2ln (5^{x+1} +e^{x})*\dfrac{1}{5^{x+1} +e^{x}}*(5^{x+1}ln5*1+e^x*1)=\dfrac{2ln (5^{x+1} +e^{x})*(5^{x+1}ln5+e^x)}{5^{x+1} +e^{x}}$

$2)(-x^{e}+tg(ln(8x^{2}+5x)))'=-ex^{e-1}+\dfrac{1}{cos^2(ln(8x^{2}+5x))}*\dfrac{1}{8x^{2}+5x}*(16x+5)$

$3) (( \dfrac{1+x^{6} }{x^{2}-6 })^{3})'=3*( \dfrac{1+x^{6} }{x^{2}-6 })^2*\dfrac{6x^5*(x^2-6)-(1+x^6)*2x}{(x^2-6)^2}=3*( \dfrac{1+x^{6} }{x^{2}-6 })^2*\dfrac{4x^7-36x^5-2x}{(x^2-6)^2}$

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hulahupa спс

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