Solve (y+sqrt{6})(y-sqrt{6})

$$( y + \sqrt { 6 } ) ( y - \sqrt { 6 } )$$

Evaluate

$$y^{2}-6$$

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}.

$$y^{2}-\left(\sqrt{6}\right)^{2}$$

The square of \sqrt{6} is 6.

$$y^{2}-6$$

Differentiate w.r.t. y

$$2y$$

Steps Using Derivative Rule for Sum

Consider \left(y+\sqrt{6}\right)\left(y-\sqrt{6}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}-\left(\sqrt{6}\right)^{2})$$

The square of \sqrt{6} is 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{2}-6)$$

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}.

$$2y^{2-1}$$

Subtract 1 from 2.

$$2y^{1}$$

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

$$2y$$