Solve (7x+sqrt{22})*(7x-sqrt{22})=

$$( 7 x + \sqrt { 22 } ) \cdot ( 7 x - \sqrt { 22 } ) =$$

Evaluate

$$49x^{2}-22$$

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}.

$$\left(7x\right)^{2}-\left(\sqrt{22}\right)^{2}$$

Expand \left(7x\right)^{2}.

$$7^{2}x^{2}-\left(\sqrt{22}\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

$$49x^{2}-\left(\sqrt{22}\right)^{2}$$

The square of \sqrt{22} is 22.

$$49x^{2}-22$$

Differentiate w.r.t. x

$$98x$$

Steps Using Derivative Rule for Sum

Consider \left(7x+\sqrt{22}\right)\left(7x-\sqrt{22}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(7x\right)^{2}-\left(\sqrt{22}\right)^{2})$$

Expand \left(7x\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7^{2}x^{2}-\left(\sqrt{22}\right)^{2})$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(49x^{2}-\left(\sqrt{22}\right)^{2})$$

The square of \sqrt{22} is 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(49x^{2}-22)$$

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}.

$$2\times 49x^{2-1}$$

Multiply 2 times 49.

$$98x^{2-1}$$

Subtract 1 from 2.

$$98x^{1}$$

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

$$98x$$