If x and y satisfies the equation \(\rm y^{2\over3} + x^{3\over2} + 3

1.	If x and y satisfies the equation \(\rm y^{2\over3} + x^{3\over2} + 3x^2 = 0\), then find the value of \(\rm dy\over dx\)1. \(\rm -{9\over4}x^{1\over2}y^{1\over3} + 9xy^{1\over3}\)2. \(\rm -{9\over4}x^{1\over2} + 9x\)3. \(\rm {9\over4}x^{1\over2}y^{1\over3} + 6xy^{1\over3}\)4. \(\rm -{9\over4}x^{1\over2}y^{1\over3} -9xy^{1\over3}\)
Answer» Correct Answer - Option 4 : \(\rm -{9\over4}x^{1\over2}y^{1\over3} -9xy^{1\over3}\) Concept: \(\rm d\over dx\)xn = nxn-1 Calculation: Given \(\rm y^{2\over3} + x^{3\over2} + 3x^2 = 0\) Differentiating with respect to x \(\rm {2\over3}(y^{-1\over3}){dy\over dx} + {3\over2}(x^{1\over2}) + 3(2x) = 0\) \(\rm {2\over3y^{1\over3}}{dy\over dx} = -{3\over2}x^{1\over2} -6x\) \(\rm {dy\over dx} = {3y^{1\over3}\over2}\left[-{3\over2}x^{1\over2} -6x\right]\) \(\rm {dy\over dx} = -{9\over4}x^{1\over2}y^{1\over3} -9xy^{1\over3}\)

If x and y satisfies the equation \(\rm y^{2\over3} + x^{3\over2} + 3x^2 = 0\), then find the value of \(\rm dy\over dx\)1. \(\rm -{9\over4}x^{1\over2}y^{1\over3} + 9xy^{1\over3}\)2. \(\rm -{9\over4}x^{1\over2} + 9x\)3. \(\rm {9\over4}x^{1\over2}y^{1\over3} + 6xy^{1\over3}\)4. \(\rm -{9\over4}x^{1\over2}y^{1\over3} -9xy^{1\over3}\)

Answer» Correct Answer - Option 4 : \(\rm -{9\over4}x^{1\over2}y^{1\over3} -9xy^{1\over3}\)

Concept:

\(\rm d\over dx\)xn = nxn-1

Calculation:

Given \(\rm y^{2\over3} + x^{3\over2} + 3x^2 = 0\)

Differentiating with respect to x

\(\rm {2\over3}(y^{-1\over3}){dy\over dx} + {3\over2}(x^{1\over2}) + 3(2x) = 0\)

\(\rm {2\over3y^{1\over3}}{dy\over dx} = -{3\over2}x^{1\over2} -6x\)

\(\rm {dy\over dx} = {3y^{1\over3}\over2}\left[-{3\over2}x^{1\over2} -6x\right]\)

\(\rm {dy\over dx} = -{9\over4}x^{1\over2}y^{1\over3} -9xy^{1\over3}\)

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