If y = x + e^x , then d^2 x dy^2 is equal to

Step-by-step solution

Given y = x + e^x Differentiating with respect to x : dy dx = 1 + e^x Taking the reciprocal: dx dy = 1 1 + e^x Differentiating with respect to y : d^2 x dy^2 = d dy ( dx dy ) = d dx ( dx dy ) dx dy Substituting the values: d^2 x dy^2 = d dx ( 1 1 + e^x ) ( 1 1 + e^x ) d^2 x dy^2 = ( -e^x (1 + e^x)^2 ) ( 1 1 + e^x ) d^2 x dy^2 = -e^x (1 + e^x)^3 Answer: -e^x (1 + e^x)^3