If y= x a + a x , then 2 x y d y d x is equal to

Step-by-step solution

Given y = x a + a x = x a + a x . Differentiating with respect to x : dy dx = 1 a 1 2 x + a ( - 1 2 x^ -3/2 ) dy dx = 1 2 ax - a 2x x = 1 2 ax - a 2x x a a = 1 2 ax - a 2x ax dy dx = 1 2 ax ( 1 - a x ) = 1 2 ax ( x-a x ) Now, calculate 2xy dy dx : 2xy dy dx = 2x ( x a + a x ) 1 2 ax ( x-a x ) 2xy dy dx = 2x ( x+a ax ) 1 2 ax ( x-a x ) 2xy dy dx = 2x(x+a)(x-a) 2ax x = x^2-a^2 ax = x a - a x . Answer: x a - a x