Derivative Calculator

ืžื›ื™ืœ ืžื•ื“ืขื•ืช
+10Kโ€
ื”ื•ืจื“ื•ืช
ืกื™ื•ื•ื’ ืชื•ื›ืŸ
ื›ื•ืœื
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš

ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ืžื—ืฉื‘ื•ืŸ ื ื’ื–ืจื•ืช ืžืืคืฉืจ ืœืš ืœืคืชื•ืจ ืžืฉื•ื•ืื•ืช ื ื’ื–ืจื•ืช ืคื•ื ืงืฆื™ื•ื ืœื™ื•ืช. ืืชื” ื™ื›ื•ืœ ืœืคืชื•ืจ ื’ื–ื™ืจื” ื•ืœืงื‘ืœ ืคืชืจื•ื ื•ืช ืฉืœื‘ ืื—ืจ ืฉืœื‘ ืขื ืžื—ืฉื‘ื•ืŸ ืžืชืžื˜ื™ ื–ื”.

ื”ืžื˜ืจื” ืฉืœ ื™ืฆื™ืจืช ื”ืืคืœื™ืงืฆื™ื” ื”ื—ื™ื ืžื™ืช ื”ื–ื• ื”ื™ื ืœืกืคืง ืœืš ืืช ื”ื“ืจืš ื”ืงืœื” ื‘ื™ื•ืชืจ ืœืคืชื•ืจ ื ื’ื–ืจื•ืช. ื–ื” ืžืืคืฉืจ ืœืš ืœื”ืชืืžืŸ ืขืœ ื™ื“ื™ ืžืชืŸ ื”ืžืฉื™ืžื” ื”ืžืœืื” ืื• ื‘ืžื™ืœื™ื ืคืฉื•ื˜ื•ืช ื™ื•ืชืจ ืขืœ ื™ื“ื™ ืฉื™ืžื•ืฉ ื‘ื”ื‘ื—ื ื” ืฉืœื‘ ืื—ืจ ืฉืœื‘. ืžื—ืฉื‘ื•ืŸ ื’ื–ื™ืจื” ื–ื” ืžืกืคืง ื—ื™ืฉื•ื‘ ื ื’ื–ืจืช ืจืืฉื•ื ื”, ืฉื ื™ื™ื”, ืฉืœื™ืฉื™ืช, ืจื‘ื™ืขื™ืช ื•ื—ืžื™ืฉื™ืช, ื›ืžื• ื’ื ืคื•ื ืงืฆื™ื•ืช ืžื‘ื“ืœืช ืฉืœ ืžืฉืชื ื™ื ืจื‘ื™ื (ื ื’ื–ืจื•ืช ื—ืœืงื™ื•ืช) ื•ืื•ืžื“ืŸ ืฉืœ ืฉื•ืจืฉื™ื/ืืคืกื™ื. ืืชื” ื™ื›ื•ืœ ืืคื™ืœื• ืœืขื™ื™ืŸ ื‘ืชืฉื•ื‘ื•ืช ืฉืœืš ืขืœ ื™ื“ื™ ืžื—ืฉื‘ื•ืŸ ื–ื”.

ืชื›ื•ื ื•ืช ืฉืœ ืžื—ืฉื‘ื•ืŸ ื ื’ื–ืจื•ืช ืขื ืฉืœื‘ื™ื
ืœื”ืœืŸ ื›ืžื” ืชื›ื•ื ื•ืช ืขื™ืงืจื™ื•ืช ืฉืœ ืืคืœื™ืงืฆื™ื™ืช ืคืชืจื•ืŸ ื ื’ื–ืจืช ื–ื•. ืื ื• ื‘ื˜ื•ื—ื™ื ืฉืชืžืฆืื• ื‘ื• ื“ื‘ืจื™ื ืžื•ืขื™ืœื™ื ืจื‘ื™ื ื™ื•ืชืจ, ืœืื—ืจ ื”ืฉื™ืžื•ืฉ ื‘ืคื•ืชืจ ื”ื ื’ื–ืจื•ืช.

ื”ื˜ื•ื‘ ื‘ื™ื•ืชืจ ืœืกื˜ื•ื“ื ื˜ื™ื
ื–ื” ืงื“ื—ืชื ื™ ืขื‘ื•ืจ ืชืœืžื™ื“ื™ื ืœืคืชื•ืจ ื™ื“ื ื™ืช ืืช ื”ื’ื–ื™ืจื”. ื›ื™ื•ื, ืคืชืจื•ืŸ ืœื›ืœ ื“ื™ืœืžื” ื ืžืฆื ื‘ืขื™ื“ืŸ ื”ื˜ื›ื ื•ืœื•ื’ื™ื” ื•ื”ืžื—ืงืจ. ื”ื ื’ื–ืจืช ื™ื›ื•ืœื” ืœื—ืฉื‘ ื‘ืงืœื•ืช ืฆืขื“ ืื—ืจ ืฆืขื“ ืขื ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•.

ืคืชืจื•ืŸ ืžื“ื•ื™ืง
ื–ื”ื• ืžื—ืฉื‘ื•ืŸ ื ื’ื–ืจื•ืช ืขื ืคืชืจื•ืŸ ื”ื’ื•ืŸ, ืฉืขื•ื–ืจ ืœื”ื™ืžื ืข ืžืžืœื›ื•ื“ื•ืช ื•ืœื‘ื ื•ืช ืืช ื”ื‘ื™ื˜ื—ื•ืŸ ืฉืœืš ื‘ืชืฉื•ื‘ื•ืช ืฉืœืš. ืืชื” ื™ื›ื•ืœ ืœืกืžื•ืš ืขืœ ื”ืคืชืจื•ืŸ ืฉื ื™ืชืŸ ืขืœ ื™ื“ื™ ืžื—ืฉื‘ื•ืŸ ื–ื” ืžื›ื™ื•ื•ืŸ ืฉื”ื•ื ื ื•ืชืŸ ืœืš ืคืชืจื•ืŸ ืฉืœื‘ ืื—ืจ ืฉืœื‘. ื›ืš ืฉืชื•ื›ืœ ืœืžื“ื•ื“ ืืช ื–ื” ื‘ืงืœื•ืช.

ืคื•ืชืจ ื ื’ื–ืจื•ืช ืงืœ ืœืฉื™ืžื•ืฉ
ืžื›ืœ ืฉืืจ ื”ืžื—ืฉื‘ื•ื ื™ื, ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื• ื“ื™ ืžื•ืขื™ืœื”. ื›ื™ ื–ื” ืงืœ ืœืฉื™ืžื•ืฉ ื•ื›ืžืขื˜ ื›ืœ ืื—ื“ ื™ื›ื•ืœ ืœืงื‘ืœ ื’ื™ืฉื” ืืœื™ื•. ืชื’ืœื• ืฉื”ื•ื ืžื•ืชืื ื‘ืื•ืคืŸ ืื™ื“ื™ืืœื™ ืœืžืคืจื˜ื™ื ืฉืœื›ื.

ืžื—ืฉื‘ื•ืŸ ื ื’ื–ืจื•ืช ืฉืœื‘ ืื—ืจ ืฉืœื‘
ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื• ืœื•ืงื—ืช ื ื’ื–ืจื•ืช ืขื ืฉืœื‘ื™ื, ื•ืžืฆื™ื’ื” ื”ืกื‘ืจื™ื ื‘ืฆื•ืจื” ืคืฉื•ื˜ื” ื™ื•ืชืจ ื›ื“ื™ ืฉืœื ืชืชื‘ืœื‘ืœื•. ืขืงืจื•ื ื•ืช ื”ื”ื‘ื—ื ื” ื”ืคืฉื•ื˜ื™ื, ื›ื•ืœืœ ื”ื›ืœืœ ื”ืงื‘ื•ืข, ื›ืœืœ ื”ืกื›ื•ื, ื›ืœืœ ื”ืžื•ืฆืจ, ื›ืœืœ ื”ืžื ื”, ื›ืœืœ ื”ืฉืจืฉืจืช ื•ื›ืœืœ ื”ื›ื•ื—, ื˜ืขื•ื ื™ื ืžืจืืฉ.

ืืคืœื™ืงืฆื™ื™ืช ืคืชืจื•ืŸ ื ื’ื–ืจื•ืช ืžืœื
ื ื’ื–ืจื•ืช ืžืฉื•ื•ืื•ืช ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช, ื”ืคื•ืš-ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช, ืืงืกืคื•ื ื ืฆื™ืืœื™ื•ืช, ืฉื•ืจืฉ ืจื™ื‘ื•ืขื™ื•ืช ื•ืœื•ื’ืจื™ืชืžื™ื•ืช ื”ืŸ ื”ื‘ื™ื˜ื•ื™ื™ื ื”ื™ื“ื•ืขื™ื ื‘ื™ื•ืชืจ ืฉื“ื•ืจืฉื™ื ืœืคืชื•ืจ ืขืœ ื™ื“ื™ ืคื•ืชืจ ื ื’ื–ืจืช ืขื ืคืชืจื•ืŸ. ื•ืœืžื˜ืจื” ื–ื•, ืžื—ืฉื‘ื•ืŸ ื”ื’ื–ื™ืจื” ื”ื–ื” ื™ื›ื•ืœ ืœื”ื™ื•ืช ื”ืืคืฉืจื•ืช ื”ื˜ื•ื‘ื” ื‘ื™ื•ืชืจ.

ืคื•ืชืจ ื ื’ื–ืจื•ืช ืžืชืžื˜ื™ื•ืช
ืžื—ืฉื‘ื•ืŸ ื ื’ื–ืจื•ืช ื–ื” ืขื ืคืชืจื•ืŸ ื™ื—ืฉื‘ ื›ืœ ืกื•ื’ ืฉืœ ื‘ื™ื˜ื•ื™ ื ื’ื–ืจืช ืชื•ืš ืฉื ื™ื•ืช ืกืคื•ืจื•ืช. ื”ืžื—ืฉื‘ื•ืŸ ื”ื—ื™ื ืžื™ ื”ื–ื” ื’ื ืžืงืœ ืขืœ ืคืชืจื•ืŸ ื’ื–ื™ืจื” 1, 2 ื•-5 ื™ื—ื“ ืขื ืคื•ื ืงืฆื™ื•ืช ื“ื™ืคืจื ืฆื™ืืœื™ื•ืช ืžืจื•ื‘ื•ืช ืžืฉืชื ื™ื.

ืื™ืš ืคื•ืชืจื™ื ื ื’ื–ืจื™ื?
ืืชื” ืจืง ืฆืจื™ืš ืœื”ื›ื ื™ืก ืืช ืคื•ื ืงืฆื™ื™ืช ื”ืงืœื˜ ื”ืจืฆื•ื™ื”, ื•ืขืœ ื™ื“ื™ ืคื™ืฉื•ื˜ ื”ื—ื™ืฉื•ื‘. ืคื•ืชืจ ืžื—ืฉื‘ื•ืŸ ื ื’ื–ืจื•ืช ื–ื” ื™ื—ืฉื‘ ืืช ื”ืคืœื˜. ืœื”ืœืŸ ื”ืฉืœื‘ื™ื ื”ื—ืฉื•ื‘ื™ื ื‘ื™ื•ืชืจ ืฉืชืฆื˜ืจื›ื• ืœื“ืขืช:
โ€ข ืคืชื— ืืช ืžื—ืฉื‘ื•ืŸ ื”ื’ื–ื™ืจื” ื”ื–ื”.
โ€ข ืฆื™ื™ืŸ ืืช ื”ื‘ื™ื˜ื•ื™ ื”ืžืชืžื˜ื™ ื‘ืžื’ืจืฉ 'ืคื•ื ืงืฆื™ื”' ืขื ื”ืžืฉืชื ื” x.
โ€ข ืฉื™ื ืืช ื”ืžืกืคืจ ื‘ืฉื“ื” ื”ื ืชื•ืŸ, ื›ืžื” ืคืขืžื™ื ืืชื” ืจื•ืฆื” ืœื”ื‘ื—ื™ืŸ ื‘ื ื’ื–ืจืช.
โ€ข ืžืฆื ื•ืงื˜ื•ืจ ืฉื™ื›ื•ืœ ืœื”ื™ื•ืช x, y, z ื•ื›ืŸ ื”ืœืื”.
โ€ข ืื ื‘ืฉืœื‘ ืžืกื•ื™ื ืชื—ืœื™ื˜ ืœืขื™ื™ืŸ ื‘ืžืžืฆืื™ื, ื”ื–ืŸ ืื•ืชื ื‘ื‘ื™ืช ื”ืžืฉืคื˜ ืฉื ื™ืชืŸ, ืื—ืจืช ื”ืฉืืจ ื‘ื™ืช ืžืฉืคื˜ ื–ื” ืจื™ืง.
โ€ข ื ื•ืกื—ืช ื”ื ื’ื–ืจืช ืชืคื•ืฉื˜ ืขืœ ื™ื“ื™ ื”ืžื—ืฉื‘ื•ืŸ ื•ืชืžืฆื ืืช ื”ืคืชืจื•ืŸ ืขื ืฉืœื‘ื™ื ืชื•ืš ื–ืžืŸ ืงืฆืจ.
โ€ข ื”ืขืชืง ืื• ื”ื•ืจื“ ืืช ื”ืชื•ืฆืื•ืช ืœืฉื™ืžื•ืฉ ื‘ื›ืœ ืžืงื•ื.

ืœื ืจืง ืฉื”ืžื—ืฉื‘ื•ืŸ ื”ื–ื” ื™ื›ื•ืœ ืœืืคืฉืจ ืœืš ืœืคืชื•ืจ ื ื’ื–ืจื•ืช ืžื•ืจื›ื‘ื•ืช ืขืœ ื™ื“ื™ ืฉื™ืžื•ืฉ ื‘ื”ื‘ื—ื ื” ืื ืœื™ื˜ื™ืช, ืืœื ืฉืืชื” ื™ื›ื•ืœ ื’ื ืœื”ืฉืชืžืฉ ื‘ื”ืŸ ื›ืฉืืชื” ืœื•ืžื“ ืœืืžืช ืืช ืชืจื’ื™ืœื™ ื”ื’ื–ื™ืจื” ืฉืœืš.
ืขื“ื›ื•ืŸ ืื—ืจื•ืŸ ื‘ืชืืจื™ืš
12 ื‘ืกืคื˜ืณ 2025

ืื‘ื˜ื—ืช ื ืชื•ื ื™ื

ื›ื“ื™ ืœืฉืžื•ืจ ืขืœ ื”ื‘ื˜ื™ื—ื•ืช ืฆืจื™ืš ืงื•ื“ื ื›ืœ ืœื”ื‘ื™ืŸ ืื™ืš ื”ืžืคืชื—ื™ื ืื•ืกืคื™ื ื•ืžืฉืชืคื™ื ืืช ื”ื ืชื•ื ื™ื ืฉืœืš. ื ื•ื”ืœื™ ืคืจื˜ื™ื•ืช ื”ื ืชื•ื ื™ื ื•ืื‘ื˜ื—ืช ื”ื ืชื•ื ื™ื ืขืฉื•ื™ื™ื ืœื”ืฉืชื ื•ืช ื‘ื”ืชืื ืœืฉื™ืžื•ืฉ, ืœืื–ื•ืจ ื•ืœื’ื™ืœ ื”ืžืฉืชืžืฉ. ื”ืžืคืชื— ืกื™ืคืง ืืช ื”ืžื™ื“ืข ื”ื–ื” ื•ื”ื•ื ืขืฉื•ื™ ืœืขื“ื›ืŸ ืื•ืชื• ืžื“ื™ ืคืขื.
ื”ืืคืœื™ืงืฆื™ื” ื”ื–ืืช ืขืฉื•ื™ื” ืœืฉืชืฃ ืืช ืกื•ื’ื™ ื”ื ืชื•ื ื™ื ื”ืืœื” ืขื ืฆื“ื“ื™ื ืฉืœื™ืฉื™ื™ื
ืžื–ื”ื” ื”ืžื›ืฉื™ืจ ืื• ืžื–ื”ื™ื ืื—ืจื™ื
ื”ื ืชื•ื ื™ื ืžื•ืฆืคื ื™ื ื‘ื–ืžืŸ ื”ื”ืขื‘ืจื”
ืื™ ืืคืฉืจ ืœืžื—ื•ืง ืืช ื”ื ืชื•ื ื™ื