Solve 4x^2-4sqrt{3}x+3

$$4 x ^ { 2 } - 4 \sqrt { 3 } x + 3$$

Differentiate w.r.t. x

$$8x-4\sqrt{3}$$

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}.

$$2\times 4x^{2-1}+\left(-4\sqrt{3}\right)x^{1-1}$$

Multiply 2 times 4.

$$8x^{2-1}+\left(-4\sqrt{3}\right)x^{1-1}$$

Subtract 1 from 2.

$$8x^{1}+\left(-4\sqrt{3}\right)x^{1-1}$$

Subtract 1 from 1.

$$8x^{1}+\left(-4\sqrt{3}\right)x^{0}$$

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

$$8x+\left(-4\sqrt{3}\right)x^{0}$$

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

$$8x+\left(-4\sqrt{3}\right)\times 1$$

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

$$8x-4\sqrt{3}$$

Evaluate

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

Solution Steps

Multiply -1 and 4 to get -4.

$$4x^{2}-4\sqrt{3}x+3$$