Question

$\huge{\sf{\bf{\tt{\dfrac{d}{dx}\left(e^{2x}\right)}}}}$

easy hard question !!

??

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\large{\boxed{\bf{\dfrac{d}{dx}\left(e^{2x}\right)}}}$

♣ ᴀɴꜱᴡᴇʀ :

$\boxed{\bf{\dfrac{d}{dx}\left(e^{2x}\right)=e^{2x}\cdot \:2}}}$

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ :

$\Rightarrow \sf { Apply\:\: the \:\:chain\:\: rule: \dfrac{d f(u)}{d x}=\dfrac{d f}{d u} \cdot \dfrac{d u}{d x}}$

$\sf{f=e^u,\:\:u=2x}$

$\sf{=\dfrac{d}{du}\left(e^u\right)\dfrac{d}{dx}\left(2x\right)}$

$\Rightarrow \sf{\dfrac{d}{du}\left(e^u\right)=e^u}$

$\sf{=e^u\dfrac{d}{dx}\left(2x\right)}$

$\sf{Substitute\:back\:u=2x}$

$\sf{=e^{2x}\dfrac{d}{dx}\left(2x\right)}$

$\Rightarrow \sf{\dfrac{d}{dx}\left(2x\right) = 2}$

$\huge{\boxed{\bf{=e^{2x}\cdot \:2}}}$

Answer 2

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