Solve 2x(-1)^2-4x(-1)-1

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

Evaluate

$$6x-1$$

Solution Steps

Calculate -1 to the power of 2 and get 1.

$$2x\times 1-4x\left(-1\right)-1$$

Multiply 2 and 1 to get 2.

$$2x-4x\left(-1\right)-1$$

Multiply 4 and -1 to get -4.

$$2x-\left(-4x\right)-1$$

The opposite of -4x is 4x.

$$2x+4x-1$$

Combine 2x and 4x to get 6x.

$$6x-1$$

Differentiate w.r.t. x

$$6$$

Steps Using Derivative Rule for Sum

Calculate -1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x\times 1-4x\left(-1\right)-1)$$

Multiply 2 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-4x\left(-1\right)-1)$$

Multiply 4 and -1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-\left(-4x\right)-1)$$

The opposite of -4x is 4x.

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

Combine 2x and 4x to get 6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x-1)$$

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}.

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$