Solve (x^1/2+2)+(-2x^1/2+3)

$$( x ^ { 1 / 2 } + 2 ) + ( - 2 x ^ { 1 / 2 } + 3 )$$

Evaluate

$$-\sqrt{x}+5$$

Solution Steps

Combine x^{\frac{1}{2}} and -2x^{\frac{1}{2}} to get -x^{\frac{1}{2}}.

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

Add 2 and 3 to get 5.

$$-x^{\frac{1}{2}}+5$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Combine x^{\frac{1}{2}} and -2x^{\frac{1}{2}} to get -x^{\frac{1}{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{\frac{1}{2}}+2+3)$$

Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{\frac{1}{2}}+5)$$

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}.

$$\frac{1}{2}\left(-1\right)x^{\frac{1}{2}-1}$$

Multiply \frac{1}{2} times -1.

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

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

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