Solve (sqrt{2x}+5)(sqrt{2x}-5)

$$( \sqrt { 2 x } + 5 ) ( \sqrt { 2 x } - 5 )$$

Evaluate

$$2x-25$$

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}.

$$\left(\sqrt{2x}\right)^{2}-5^{2}$$

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

$$2x-5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$2x-25$$

Differentiate w.r.t. x

$$2$$

Steps Using Derivative Rule for Sum

Consider \left(\sqrt{2x}+5\right)\left(\sqrt{2x}-5\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\sqrt{2x}\right)^{2}-5^{2})$$

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

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

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-25)$$

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}.

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

Subtract 1 from 1.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$