Let y = [p] x^3 y . If dy dx = 3 2 when y = 1 , then the value of p is equal to

Step-by-step solution

Given y = [p] x^3 y Raising both sides to the power p : y^p = x^3 y y^ p-1 = x^3 Differentiating both sides with respect to x : (p-1) y^ p-2 dy dx = 3x^2 When y = 1 , from y^ p-1 = x^3 , we get x^3 = 1 x = 1 . Substituting x = 1 , y = 1 , and dy dx = 3 2 into the differentiated equation: (p-1) (1)^ p-2 ( 3 2 ) = 3(1)^2 (p-1) 3 2 = 3 p - 1 = 2 p = 3 Answer: 3