Solve 11x^2-2sqrt{11}x+1

$$11 { x }^{ 2 } -2 \sqrt{ 11 } x+1$$

Differentiate w.r.t. x

$$22x-2\sqrt{11}$$

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}.

$$2\times 11x^{2-1}+\left(-2\sqrt{11}\right)x^{1-1}$$

Multiply 2 times 11.

$$22x^{2-1}+\left(-2\sqrt{11}\right)x^{1-1}$$

Subtract 1 from 2.

$$22x^{1}+\left(-2\sqrt{11}\right)x^{1-1}$$

Subtract 1 from 1.

$$22x^{1}+\left(-2\sqrt{11}\right)x^{0}$$

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

$$22x+\left(-2\sqrt{11}\right)x^{0}$$

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

$$22x+\left(-2\sqrt{11}\right)\times 1$$

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

$$22x-2\sqrt{11}$$

Evaluate

$$11x^{2}-2\sqrt{11}x+1$$

Solution Steps

Multiply -1 and 2 to get -2.

$$11x^{2}-2\sqrt{11}x+1$$