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ника2911
@ника2911
July 2021
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найти производные функций:
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m11m
A) y' = (x³)' (3lnx-1)+x³(3lnx-1)' - [
(x+1)' *e^(x) - (e^(x))' (x+1)
] =
e^(x)*e^(x)
=3x² (3lnx-1) + x³ * 3 * (1/x) - [
e^(x) - e^(x)(x+1)
] =
e^(x)*e^(x)
= 9x² lnx - 3x² +3x² -
e^(x) (1-x-1)
=
e^(x)*e^(x)
= 9x² lnx +
x
e^(x)
б) y' = 4 * (5^(tg2x)+3)³ * 5^(tg2x) * ln5 *
2
=
cos²2x
=
8 (5^(tg2x)+3)³ * 5^(tg2x) * ln5
cos²2x
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Answers & Comments
e^(x)*e^(x)
=3x² (3lnx-1) + x³ * 3 * (1/x) - [ e^(x) - e^(x)(x+1)] =
e^(x)*e^(x)
= 9x² lnx - 3x² +3x² - e^(x) (1-x-1) =
e^(x)*e^(x)
= 9x² lnx + x
e^(x)
б) y' = 4 * (5^(tg2x)+3)³ * 5^(tg2x) * ln5 * 2 =
cos²2x
= 8 (5^(tg2x)+3)³ * 5^(tg2x) * ln5
cos²2x