Solve m^2-2sqrt{3}m+3

$$m ^ { 2 } - 2 \sqrt { 3 } m + 3$$

Differentiate w.r.t. m

$$2\left(m-\sqrt{3}\right)$$

Steps Using Derivative Rule for Sum

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}.

$$2m^{2-1}+\left(-2\sqrt{3}\right)m^{1-1}$$

Subtract 1 from 2.

$$2m^{1}+\left(-2\sqrt{3}\right)m^{1-1}$$

Subtract 1 from 1.

$$2m^{1}+\left(-2\sqrt{3}\right)m^{0}$$

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

$$2m+\left(-2\sqrt{3}\right)m^{0}$$

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

$$2m+\left(-2\sqrt{3}\right)\times 1$$

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

$$2m-2\sqrt{3}$$

Evaluate

$$\left(m-\sqrt{3}\right)^{2}$$

Solution Steps

Multiply -1 and 2 to get -2.

$$m^{2}-2\sqrt{3}m+3$$