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Let x and y be differentiable functions of t and suppose that they are related by the equation xy-1=y^2. Find dx/dt when x=2 and d/y=1.Need the solution and answer rn​

Answer» <html><body><p><strong>Answer:</strong></p><p><a href="https://interviewquestions.tuteehub.com/tag/given-473447" style="font-weight:bold;" target="_blank" title="Click to know more about GIVEN">GIVEN</a> u=f(x,y) is a a <a href="https://interviewquestions.tuteehub.com/tag/differentiable-7726202" style="font-weight:bold;" target="_blank" title="Click to know more about DIFFERENTIABLE">DIFFERENTIABLE</a> function of x and y, where x,y are differentiable functions of t.</p><p></p><p>We have to <a href="https://interviewquestions.tuteehub.com/tag/find-11616" style="font-weight:bold;" target="_blank" title="Click to know more about FIND">FIND</a> </p><p>dt</p><p>du</p><p></p><p> </p><p></p><p>Since x,y are differentiable functions of t</p><p></p><p>Let x=g(t),y=h(t)</p><p></p><p><a href="https://interviewquestions.tuteehub.com/tag/thus-2307358" style="font-weight:bold;" target="_blank" title="Click to know more about THUS">THUS</a> by chain <a href="https://interviewquestions.tuteehub.com/tag/rule-1192038" style="font-weight:bold;" target="_blank" title="Click to know more about RULE">RULE</a> we get</p><p></p><p>dt</p><p>du</p><p></p><p> = </p><p>∂x</p><p>∂f</p><p></p><p> ⋅ </p><p>dt</p><p>dx</p><p></p><p> + </p><p>∂y</p><p>∂f</p><p></p><p> ⋅ </p><p>dt</p><p>dy</p><p></p><p> </p><p></p></body></html>


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