Solve 36x^2-12sqrt{3}x-5

$$36 x ^ { 2 } - 12 \sqrt { 3 } x - 5$$

Differentiate w.r.t. x

$$72x-12\sqrt{3}$$

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}.

$$2\times 36x^{2-1}+\left(-12\sqrt{3}\right)x^{1-1}$$

Multiply 2 times 36.

$$72x^{2-1}+\left(-12\sqrt{3}\right)x^{1-1}$$

Subtract 1 from 2.

$$72x^{1}+\left(-12\sqrt{3}\right)x^{1-1}$$

Subtract 1 from 1.

$$72x^{1}+\left(-12\sqrt{3}\right)x^{0}$$

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

$$72x+\left(-12\sqrt{3}\right)x^{0}$$

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

$$72x+\left(-12\sqrt{3}\right)\times 1$$

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

$$72x-12\sqrt{3}$$

Evaluate

$$36x^{2}-12\sqrt{3}x-5$$

Solution Steps

Multiply -1 and 12 to get -12.

$$36x^{2}-12\sqrt{3}x-5$$