Question

what is f'(x) ????????​

Answer 1

• ᴀɴꜱᴡᴇʀ :

ꜰ'(x) ꜱɪᴍᴘʟʏ ᴍᴇᴀɴꜱ ᴛʜᴇ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏꜰ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ 'ꜰ' ᴡɪᴛʜ ʀᴇꜱᴘᴇᴄᴛ ᴛᴏ ᴠᴀʀɪᴀʙʟᴇ 'x'.

ɪɴ ʟᴀʏᴍᴀɴ ᴛᴇʀᴍꜱ, ꜰ'(x) ɪꜱ ᴛʜᴇ ʀᴀᴛᴇ ᴏꜰ ᴄʜᴀɴɢᴇ ᴏꜰ ꜰᴜɴᴄᴛɪᴏɴ 'ꜰ' ᴡɪᴛʜ ʀᴇꜱᴘᴇᴄᴛ ᴛᴏ ᴄʜᴀɴɢᴇ ɪɴ ᴛʜᴇ ᴠᴀʀɪᴀʙʟᴇ 'x'.

ɪᴛ ɪꜱ ᴀʟꜱᴏ ᴜꜱᴇᴅ ᴛᴏ ᴅᴇꜱᴄʀɪʙᴇ ᴛʜᴇ ꜱʟᴏᴘᴇ ᴏꜰ ᴛᴀɴɢᴇɴᴛ ᴏꜰ ᴀ ꜰᴜɴᴄᴛɪᴏɴ ꜰ. ʜᴏᴘᴇ ᴛʜᴇ ᴀɴꜱᴡᴇʀ ʜᴇʟᴘꜱ.

• ᴇxᴘʟᴀɴᴀᴛɪᴏɴ

ɪᴛ ᴄᴀɴ ᴄᴀʀʀʏ 2 ᴍᴇᴀɴɪɴɢꜱ ɪɴ ᴍᴀᴛʜ ᴛʜᴀᴛ ɪ ʜᴀᴠᴇ ꜱᴇᴇɴ

• ɪɴ ᴄᴀʟᴄᴜʟᴜꜱ ᴀɴ ᴀᴘᴏꜱᴛʀᴏᴘʜᴇ ᴄᴀɴ ʙᴇ ᴜꜱᴇᴅ ᴛᴏ ᴅᴇɴᴏᴛᴇ ᴛʜᴇ ꜰɪʀꜱᴛ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏꜰ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ɪᴛ ᴀᴘᴘʟɪᴇꜱ ᴛᴏ, ᴡʜᴇʀᴇ ɪᴛ ɪꜱ ɪꜱ ᴇɪᴛʜᴇʀ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ɴᴀᴍᴇ & ɪᴛ’ꜱ ᴅᴏᴍᴀɪɴ, ᴀɴᴅ/ᴏʀ ꜰɪʀꜱᴛ ᴅᴇʀɪᴠᴀᴛɪᴠᴇ ᴏꜰ ʜᴏʟᴏᴍᴏʀᴘʜɪꜱᴍꜱ, ᴏʀ ᴊᴜꜱᴛ ᴀꜰᴛᴇʀ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ɴᴀᴍᴇ - ʟɪᴋᴇ ꜰ’ = …..

• ɪɴ ᴀxɪᴏᴍᴀᴛɪᴄ ᴏʀ ɴᴀɪᴠᴇ ꜱᴇᴛ ᴛʜᴇᴏʀʏ, ɪᴛ ʀᴇᴘʀᴇꜱᴇɴᴛꜱ ᴛʜᴇ ᴄᴏᴍᴘʟᴇᴍᴇɴᴛ ᴏꜰ ᴀ ꜱᴇᴛ. ɪꜰ ꜰ(x) ɪꜱ ᴀ ꜱᴇᴛ ᴍᴀᴅᴇ ᴜᴘ ᴏꜰ ᴀ ᴄᴏʟʟᴇᴄᴛɪᴏɴ ᴏꜰ ᴍᴇᴍʙᴇʀꜱ, x, ᴛʜᴇɴ ꜰ’(x) ɪꜱ ᴛʜᴇ ꜱᴇᴛ ᴏꜰ ᴀʟʟ ɪᴛᴇᴍꜱ ᴛʜᴀᴛ ᴅᴏ ɴᴏᴛ ʙᴇʟᴏɴɢ ᴛᴏ ꜰ.

ᴛʜᴇ ᴇxᴘʀᴇꜱꜱɪᴏɴ "ꜰ (x)" ᴍᴇᴀɴꜱ "ᴀ ꜰᴏʀᴍᴜʟᴀ, ɴᴀᴍᴇᴅ ꜰ, ʜᴀꜱ x ᴀꜱ ɪᴛꜱ ɪɴᴘᴜᴛ ᴠᴀʀɪᴀʙʟᴇ". ɪᴛ ᴅᴏᴇꜱ ɴᴏᴛ ᴍᴇᴀɴ "ᴍᴜʟᴛɪᴘʟʏ ꜰ ᴀɴᴅ x"! ᴅᴏɴ'ᴛ ᴇᴍʙᴀʀʀᴀꜱꜱ ʏᴏᴜʀꜱᴇʟꜰ ʙʏ ᴘʀᴏɴᴏᴜɴᴄɪɴɢ (ᴏʀ ᴛʜɪɴᴋɪɴɢ ᴏꜰ) "ꜰ (x)" ᴀꜱ ʙᴇɪɴɢ "ꜰ ᴛɪᴍᴇꜱ x", ᴀɴᴅ ɴᴇᴠᴇʀ ᴛʀʏ ᴛᴏ "ᴍᴜʟᴛɪᴘʟʏ" ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ɴᴀᴍᴇ ᴡɪᴛʜ ɪᴛꜱ ᴘᴀʀᴇɴᴛʜᴇꜱɪꜱᴇᴅ ɪɴᴘᴜᴛ.