Solve 3x+2(sqrt{x}-1(sqrt{x}-1))

$$3 x + 2 ( \sqrt { x } - 1 ( \sqrt { x } - 1 ) )$$

Evaluate

$$3x+2$$

Solution Steps

Multiply -1 and 1 to get -1.

$$3x+2\left(\sqrt{x}-\left(\sqrt{x}-1\right)\right)$$

To find the opposite of \sqrt{x}-1, find the opposite of each term.

$$3x+2\left(\sqrt{x}-\sqrt{x}-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$3x+2\left(\sqrt{x}-\sqrt{x}+1\right)$$

Combine \sqrt{x} and -\sqrt{x} to get 0.

$$3x+2\times 1$$

Multiply 2 and 1 to get 2.

$$3x+2$$

Differentiate w.r.t. x

$$3$$

Steps Using Derivative Rule for Sum

Multiply -1 and 1 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+2\left(\sqrt{x}-\left(\sqrt{x}-1\right)\right))$$

To find the opposite of \sqrt{x}-1, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+2\left(\sqrt{x}-\sqrt{x}-\left(-1\right)\right))$$

The opposite of -1 is 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+2\left(\sqrt{x}-\sqrt{x}+1\right))$$

Combine \sqrt{x} and -\sqrt{x} to get 0.

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

Multiply 2 and 1 to get 2.

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

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}.

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$