MHT CET · Maths · Differentiation
If \(x^{\frac{2}{5}}+\mathrm{y}^{\frac{2}{5}}=a^{\frac{2}{5}}\) then \(\frac{\mathrm{dy}}{\mathrm{d} x}=\)
- A \(\sqrt[5]{\left(\frac{\mathrm{y}}{x}\right)^3}\)
- B \(-\sqrt[5]{\left(\frac{x}{y}\right)^3}\)
- C \(\sqrt[5]{\left(\frac{x}{y}\right)^3}\)
- D \(-\sqrt[5]{\left(\frac{y}{x}\right)^3}\)
Answer & Solution
Correct Answer
(D) \(-\sqrt[5]{\left(\frac{y}{x}\right)^3}\)
Step-by-step Solution
Detailed explanation
\(\frac{2}{5}x^{-\frac{3}{5}} + \frac{2}{5}y^{-\frac{3}{5}}\frac{\mathrm{dy}}{\mathrm{d} x} = 0\) \(\frac{\mathrm{dy}}{\mathrm{d} x} = -\frac{x^{-\frac{3}{5}}}{y^{-\frac{3}{5}}}\)
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