Physics, asked by poonamrai8282, 7 months ago

if x=t^3+1/t2 then dx/dt is? ​

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Answered by Anonymous
54

Solution:-

We have

 \rm \: if \: x =  {t}^{3}  +  \dfrac{1}{ {t}^{2} }  \: then \:  \:  \dfrac{dx}{dt}

Now we can write as

 \rm \: x =  {t}^{3}  +  {t}^{ - 2}

Using algebra of differentiation

 \boxed{ \rm \:  \dfrac{d}{dx} (f(x)  \pm \: g(x)) =  \dfrac{d}{dx} f(x) \pm \dfrac{d}{dx} g(x)}

Now we can write

 \rm \: x =  {t}^{3}  +  {t}^{ - 2}

 \rm \dfrac{d}{dx}  {t}^{3}  + \dfrac{d}{dx}  {t}^{ - 2}

Using standard derivation

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

we get

 \rm \: 3t {}^{3 - 1}  - 2t {}^{ - 2 - 1}

 \rm \: 3 {t}^{2}  - 2t {}^{ - 3}

 \to \rm \:  3{t}^{2}  -  \dfrac{2}{ {t}^{3} }

Option 2 is correct

Answered by nimishadesai106
5

Answer:

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Explanation:

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