Solve (sqrt{x-3})^2+2

$$( \sqrt { x - 3 } ) ^ { 2 } + 2$$

Evaluate

$$x-1$$

Solution Steps

Calculate \sqrt{x-3} to the power of 2 and get x-3.

$$x-3+2$$

Add -3 and 2 to get -1.

$$x-1$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Calculate \sqrt{x-3} to the power of 2 and get x-3.

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

Add -3 and 2 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-1)$$

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}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$