Solve 3x^2-2x+4-x^2+x

$$3 x ^ { 2 } - 2 x + 4 - x ^ { 2 } + x$$

Evaluate

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

Solution Steps

Combine 3x^{2} and -x^{2} to get 2x^{2}.

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

Combine -2x and x to get -x.

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

Differentiate w.r.t. x

$$4x-1$$

Steps Using Derivative Rule for Sum

Combine 3x^{2} and -x^{2} to get 2x^{2}.

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

Combine -2x and x to get -x.

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

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}.

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

Multiply 2 times 2.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$4x^{1}-x^{0}$$

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

$$4x-x^{0}$$

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

$$4x-1$$