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Bimbo A.

Calculus 1 / AB

2 months, 1 week ago

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IIT(BHU), Varanasi


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Video Transcript

Yeah. Hello. So the question is suppose why? It depends implicitly on X. Given that why is we can write his ass by affects use implicit differentiation to calculate the derivative by poem of the equation implicit derivative means Y is also a function of us. It means why has internal dependency on X. So and given that equation is three X squared minus full wide square is equal to five way. And we need to evaluate pipeline that is equal to divide over the X. We know that why is a function of X. So we can differentiate it. Let us differentiate this equation with respect to us X. So D by the X off three X square -4. Y Square is equal to five and to the to be over the eggs into by because um five years just to constrain. So let us take this differentiation differential operator inside the brick. It so we get three D over the eggs X squared minus fall the over the eggs. Vice Square is equal to five. Divi Ova the X. Okay so again differentiation of X squared. Just remember that differentiation of X square will be two in two X. To the power to minus one minus and X is a function of X. So the X over dx is one and in this case it will be fall differentiation of y square is two. Y Divi over the X is equal to five and 2 divi Ova dx. So again so I'll read that is six X is equal to take this second time to the right hand side we take and take diva over the ex woman. We get five plus four multiplied by that is eight Y. So we get the value of diva over the X. If we change both of these sides, thereby over the X is equal to 6, 6/5 plus eight by which is your required answer. Or we can say the value of vibrant by prime is equal to the value of what the X. Which is the uh result of your question. By using the implicit differentiation of this clears your doubt.