Differentiate the following functions with respect to x.

Let, y =

We have to find dy/dx

As we can observe that y is a fraction of two functions say u and v where,

u = x + e^x and v = 1 + log x

∴ y = u/v

As we know that to find the derivative of fraction of two function we apply quotient rule of differentiation.

By quotient rule, we have –

…equation 1

As, u = x + e^x

∴

∵ , so we get –

⇒ …equation 2

As, v = 1 + log x

⇒ …equation 3 {∵ }

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2 and 3}

⇒

⇒

Hence,