Solve (sqrt{x}-sqrt{7})(sqrt{x}+sqrt{7})=

$$( \sqrt { x } - \sqrt { 7 } ) ( \sqrt { x } + \sqrt { 7 } ) =$$

Evaluate

$$x-7$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{x}\right)^{2}-\left(\sqrt{7}\right)^{2}$$

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

$$x-\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$x-7$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Consider \left(\sqrt{x}-\sqrt{7}\right)\left(\sqrt{x}+\sqrt{7}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\sqrt{x}\right)^{2}-\left(\sqrt{7}\right)^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-\left(\sqrt{7}\right)^{2})$$

The square of \sqrt{7} is 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-7)$$

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.

$$1$$