Math, asked by jeevith1602, 7 months ago

if u=x3y4z2, and x=t2,y=t3,z=t4,then find du/dt.​

Answers

Answered by BrainlyTornado
12

ANSWER:

\sf The \  value \  of \ \dfrac{du}{dt} =26 \ {t}^{25}

GIVEN:

  • u = x³y⁴z² , x = t², y = t³, z = t⁴.

TO FIND:

  • The value of du/dt.

EXPLANATION:

 \sf u = x^3y^4z^2

\sf \dfrac{du}{dt} = \dfrac{d}{dt}  (x^3y^4z^2)

Substitute x = t², y = t³, z = t⁴.

\sf \dfrac{du}{dt} = \dfrac{d}{dt}  (( {t}^{2})^3( {t}^{3})^4( {t}^{4})^2)

\sf \dfrac{du}{dt} = \dfrac{d}{dt}  ({t}^{6} \times {t}^{12}  \times {t}^{8})

\boxed{\bold{\large{\gray{x^m \times x^n = x^{m+n}}}}}

\sf \dfrac{du}{dt} = \dfrac{d}{dt}  ({t}^{6 + 1 2+ 8} )

\sf \dfrac{du}{dt} = \dfrac{d}{dt}  ({t}^{26} )

\boxed{ \bold{ \large{ \gray{ \dfrac{d}{dx} {x}^{n}  = n {x}^{n - 1} }}}}

\sf \dfrac{du}{dt} =26 \ {t}^{26 - 1}  \left(\dfrac{dt}{dt}  \right)

\boxed{ \bold{ \large{ \gray{ \dfrac{d}{dx}x = 1 }}}}

\sf\dfrac{du}{dt} =26 \ {t}^{25}

\sf The \  value \  of \ \dfrac{du}{dt} =26 \ {t}^{25}

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