Solve (2x^3-7x^2-3x+2)+(x-4)

$$( 2 x ^ { 3 } - 7 x ^ { 2 } - 3 x + 2 ) + ( x - 4 )$$

Evaluate

$$2x^{3}-7x^{2}-2x-2$$

Solution Steps

Combine -3x and x to get -2x.

$$2x^{3}-7x^{2}-2x+2-4$$

Subtract 4 from 2 to get -2.

$$2x^{3}-7x^{2}-2x-2$$

Differentiate w.r.t. x

$$6x^{2}-14x-2$$

Steps Using Derivative Rule for Sum

Combine -3x and x to get -2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-7x^{2}-2x+2-4)$$

Subtract 4 from 2 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-7x^{2}-2x-2)$$

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}.

$$3\times 2x^{3-1}+2\left(-7\right)x^{2-1}-2x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+2\left(-7\right)x^{2-1}-2x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+2\left(-7\right)x^{2-1}-2x^{1-1}$$

Multiply 2 times -7.

$$6x^{2}-14x^{2-1}-2x^{1-1}$$

Subtract 1 from 2.

$$6x^{2}-14x^{1}-2x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}-14x^{1}-2x^{0}$$

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

$$6x^{2}-14x-2x^{0}$$

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

$$6x^{2}-14x-2$$