If x^ 2 5 + y ^ 2 5 =a^ 2 5 then dy d x =

Step-by-step solution

Given the implicit equation x^ 2 5 + y^ 2 5 = a^ 2 5 , we seek the derivative d y d x . Differentiating both sides with respect to x , and applying the chain rule to the y term: 2 5 x^ - 3 5 + 2 5 y^ - 3 5 d y d x = 0 Solving for d y d x : 2 5 y^ - 3 5 d y d x = - 2 5 x^ - 3 5 Dividing both sides by common factors and simplifying: d y d x = - y^ 3 5 x^ 3 5 This may be expressed as d y d x = - ( y x )^ 3 5 , which matches option D.