Question

Find, dy/ dx, if x^n+y^n=a^n

Answer 1

Step-by-step explanation:

${x}^{n} + {y}^{n} = {a}^{n} \\ \\ {y}^{n} = {a}^{n} - {x}^{n} \\ \\ y = ({a}^{n} - {x}^{n})^{ \frac{1}{n} } \\ \\ \frac{dy}{dx} = \frac{d}{dx } ( ({a}^{n} - {x}^{n})^{ \frac{1}{n} } ) \\ \\ = \frac{1}{n} ({a}^{n} - {x}^{n})^{ \frac{1}{n} - 1 } \frac{d}{dx} ({a}^{n } - {x}^{n} ) \\ = \frac{1}{n} ({a}^{n} - {x}^{n}) ^{ \frac{1 - n}{n} } (0 - n {x}^{n - 1} ) \\ = - \frac{1}{n}( {a}^{n} - {x}^{n} )^{ \frac{1 - n}{n} } (n {x}^{n - 1} ) \\=-( {a}^{n} - {x}^{n} )^{ \frac{1 - n}{n} } ( {x}^{n - 1} )</p><p>$