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

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Subtract 3 from 2 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}-3x^{2}-1+x)$$

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}.

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

Multiply 3 times 2.

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

Subtract 1 from 3.

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

Multiply 2 times -3.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

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

Evaluate

$$2x^{3}-3x^{2}+x-1$$

Solution Steps

Subtract 3 from 2 to get -1.

$$2x^{3}-3x^{2}-1+x$$