Solve (5x+sqrt{60})*(5x-sqrt{60})

$$( 5 x + \sqrt { 60 } ) \cdot ( 5 x - \sqrt { 60 } )$$

Evaluate

$$25x^{2}-60$$

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}.

$$\left(5x\right)^{2}-\left(\sqrt{60}\right)^{2}$$

Expand \left(5x\right)^{2}.

$$5^{2}x^{2}-\left(\sqrt{60}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25x^{2}-\left(\sqrt{60}\right)^{2}$$

The square of \sqrt{60} is 60.

$$25x^{2}-60$$

Differentiate w.r.t. x

$$50x$$

Steps Using Derivative Rule for Sum

Consider \left(5x+\sqrt{60}\right)\left(5x-\sqrt{60}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(5x\right)^{2}-\left(\sqrt{60}\right)^{2})$$

Expand \left(5x\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5^{2}x^{2}-\left(\sqrt{60}\right)^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{2}-\left(\sqrt{60}\right)^{2})$$

The square of \sqrt{60} is 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(25x^{2}-60)$$

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}.

$$2\times 25x^{2-1}$$

Multiply 2 times 25.

$$50x^{2-1}$$

Subtract 1 from 2.

$$50x^{1}$$

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

$$50x$$