Question

${\boxed {\boxed {\bold \red{\frac{d}{dx} ({x}^{2})}}}}$



❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ
❖ ɴᴏ ꜱᴘᴀᴍᴍɪɴɢ
❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​

Answer 1

$\bold{ \frac{d}{dx} ( {x}^{2} )}$

$\bold{ ={\displaystyle \lim_{ \bold{h \to0}}} \frac{(x + h) {}^{2} + {x}^{2} }{h}}$

$\bold{ ={\displaystyle\lim_{ \bold{h \to0}}} \frac{ \cancel{ {x}^{2}} + 2xh + {h}^{2} - \cancel{{x}^{2}}}{h}}$

$\bold{ ={\displaystyle\lim_{ \bold{h \to0}}} \frac{ \cancel{h}(2xh )}{ \cancel{h}}}$

$\bold{ = 2x}$

Answer 2

Answer:

$\bold{ \frac{d}{dx} ( {x}^{2} )}$

$\bold{ ={\displaystyle \lim_{ \bold{h \to0}}} \frac{(x + h) {}^{2} + {x}^{2} }{h}}$

$\bold{ ={\displaystyle\lim_{ \bold{h \to0}}} \frac{ \cancel{ {x}^{2}} + 2xh + {h}^{2} - \cancel{{x}^{2}}}{h}}$

$\bold{ ={\displaystyle\lim_{ \bold{h \to0}}} \frac{ \cancel{h}(2xh )}{ \cancel{h}}}$

$\bold{ = 2x}$

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