find the derivative of (lnx)^3
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Step-by-step explanation:
ɪ ɢᴏᴛ
ʏ
'
=
x
ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:
ᴡᴇ ᴄᴀɴ ᴜsᴇ ᴏɴᴇ ᴏғ ᴛʜᴇ ᴘʀᴏᴘᴇʀᴛɪᴇs ᴏғ ʟᴏɢs ᴛʜᴀᴛ ᴀʟʟᴏᴡ ᴜs ᴛᴏ ᴡʀɪᴛᴇ ɪᴛ ᴀs:
ʏ
=
ʟɴ
(
x
)
ᴡᴇ ᴄᴀɴ ᴛʜᴇɴ ᴅᴇʀɪᴠᴇ ᴀs ᴜsᴜᴀʟ:
ʏ
'
=
⋅
x
ᴡᴇ ᴄᴀɴ ᴀʟsᴏ ᴜsᴇ ᴛʜᴇ ᴄʜᴀɪɴ ʀᴜʟᴇ ᴅᴇʀɪᴠɪɴɢ ᴛʜᴇ ʟᴏɢ ғɪʀsᴛ ᴀs ɪᴛ ɪs ᴀɴᴅ ᴍᴜʟᴛɪᴘʟʏ ʙʏ ᴛʜᴇ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏғ ᴛʜᴇ ᴀʀɢᴜᴍᴇɴᴛ:
ʏ
'
=
x
⋅
x
=
sɪᴍᴘʟɪғʏ:
=
x
...ᴀɢᴀɪɴ
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