Solve 2x^2-4xdivx+1

$$2 { x }^{ 2 } -4x \div x+1$$

Evaluate

$$2x^{2}-3$$

Solution Steps

Cancel out x in both numerator and denominator.

$$2x^{2}-4+1$$

Add -4 and 1 to get -3.

$$2x^{2}-3$$

Differentiate w.r.t. x

$$4x$$

Steps Using Derivative Rule for Sum

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-4+1)$$

Add -4 and 1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-3)$$

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}.

$$2\times 2x^{2-1}$$

Multiply 2 times 2.

$$4x^{2-1}$$

Subtract 1 from 2.

$$4x^{1}$$

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

$$4x$$