Solve d/dxleft({x}^frac{1{2}}+x/2+6right)

$$\frac{d}{d x } \left( { x }^{ \frac{ 1 }{ 2 } } + \frac{ x }{ 2 } +6 \right)$$

Evaluate

$$\frac{1}{2}+\frac{1}{2\sqrt{x}}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{2}x^{\frac{1}{2}-1}+\frac{1}{2}x^{1-1}$$

Subtract 1 from \frac{1}{2}.

$$\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{1}{2}x^{-\frac{1}{2}}+\frac{1}{2}$$

Differentiate w.r.t. x

$$-\frac{1}{4x^{\frac{3}{2}}}$$