#### To determine

**To find:** The derivative of
y=x+x.

#### Answer

The derivative of
y=x+x is
12x+x(1+12x).

#### Explanation

**Derivative Rules:**

**The Chain Rule:**

If *g* is differentiable at *x* and *f* is differentiable at
g(x), then the composite function
F=f∘g defined by
F(x)=f(g(x)) is differentiable at *x* and
F′ is given by the product

F′(x)=f′(g(x))⋅g′(x) (1)

(1).**Power Rule:**
ddx(xn)=nxn−1

(2).**Product Rule:**
ddx[f(x)g(x)]=f(x)ddx[g(x)]+g(x)ddx[f(x)]

(3) **Sum Rule**:
ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)]

**Calculation:**

Obtain the derivative of *y.*

y′=ddx(x+x)=ddx(x+x)12

Apply power rule and chain rule as stated above,

y′=12(x+x)12−1ddx((x+x))

Apply Sum rule and simplify as,

y′=12(x+x)[ddx(x)+ddx(x12)]=12(x+x)[(1)+12(x12−1)]=12(x+x)[(1)+12x]

Therefore, the derivative is
y=x+x is
12x+x(1+12x).