Solve (2x^2-x+1)+(54x-5-2x^2)

$$( 2 x ^ { 2 } - x + 1 ) + ( 54 x - 5 - 2 x ^ { 2 } )$$

Evaluate

$$53x-4$$

Solution Steps

Combine -x and 54x to get 53x.

$$2x^{2}+53x+1-5-2x^{2}$$

Subtract 5 from 1 to get -4.

$$2x^{2}+53x-4-2x^{2}$$

Combine 2x^{2} and -2x^{2} to get 0.

$$53x-4$$

Differentiate w.r.t. x

$$53$$

Steps Using Derivative Rule for Sum

Combine -x and 54x to get 53x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+53x+1-5-2x^{2})$$

Subtract 5 from 1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+53x-4-2x^{2})$$

Combine 2x^{2} and -2x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(53x-4)$$

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}.

$$53x^{1-1}$$

Subtract 1 from 1.

$$53x^{0}$$

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

$$53\times 1$$

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

$$53$$