Question

$\bold \red{Differentiate \: y=x^2}$


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

Answer 1

$\bold{y = {x}^{2}}$

$\bold{ \frac{Δy}{\Delta x} = { \displaystyle \lim_{Δx \to \: 0}} \: \frac{(x +Δx) {}^{2} - {x}^{2} }{Δx} }$

$\bold{{ \displaystyle \lim_{Δx \to \: 0}} \: \frac{x {}^{2} +Δx {}^{2} + 2xΔx - {x}^{2} }{Δx} }$

$\bold{{ \displaystyle \lim_{Δx \to \: 0}} \: \frac{Δx {}^{2} + 2xΔx }{Δx} }$

$\bold{{ \displaystyle \lim_{Δx \to \: 0}} \: \frac{Δx(Δx {}^{} + 2x) }{Δx} }$

$\bold{{ \displaystyle \lim_{Δx \to \: 0}} \: Δx{}^{} + 2x}$

Use limit and approximately put Δx=0

$\bold{ \frac{∂\: y}{ ∂\: x} = 2x }$

Answer 2

EVALUTION★

• $\bold \red{Differentiate \: y=x^2}$

• we know that

• $\frac{d}{dx} x = nx {}^{n - 1}$

• $\frac{d}{dx}(x) {}^{2} = 2x {}^{2 - 1} \\ \\ \\ = 2x$

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I hope it helps you