Question

Can anyone solve this
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Answer 1

Explanation:

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Answer 2

Answer:

$\bigstar{\bold{\dfrac{d}{dt} (x)=3t^{2}+8t}}$

Explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• x = t³ + 4t² + 5

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

$\dfrac{d}{dt} (x)$

$\Large{\underline{\underline{\bf{Identities\:Used:}}}}$

$\dfrac{d}{dx} (x^{n} )=nx^{n-1}$

$\dfrac{d}{dx} (x)=1$

$\dfrac{d}{dx} (constant)=0$

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ $\dfrac{d}{dt} (x) = \dfrac{d}{dt} (t^{3} +4t^{2} +5)$

→ Distributing the differential operator to all terms

$\dfrac{d}{dt} (t^{3} )+\dfrac{d}{dt}(4t^{2} )+\dfrac{d}{dt} (5)$

→ Applying the identities, we get

 $\dfrac{d}{dt} (x)=3t^{2} +4\times 2t +0$

           $=3t^{2} +8t$

$\boxed{\bold{\dfrac{d}{dt} (x)=3t^{2} +8t}}$

$\Large{\underline{\underline{\bf{More\:Identities:}}}}$

$\dfrac{d}{dx} (\sqrt{x} )=\dfrac{1}{2\sqrt{x} }$

$\dfrac{d}{dx} (\dfrac{1}{x^{n} } )=\dfrac{-n}{x^{n+1} }$