Solve 7-2x+x^3-x^2+x

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

Differentiate w.r.t. x

$$\left(x-1\right)\left(3x+1\right)$$

Steps Using Derivative Rule for Sum

Combine -2x and x to get -x.

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

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}.

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

Subtract 1 from 1.

$$-x^{0}+3x^{3-1}+2\left(-1\right)x^{2-1}$$

Subtract 1 from 3.

$$-x^{0}+3x^{2}+2\left(-1\right)x^{2-1}$$

Multiply 3 times 1.

$$-x^{0}+3x^{2}-2x^{2-1}$$

Subtract 1 from 2.

$$-x^{0}+3x^{2}-2x^{1}$$

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

$$-x^{0}+3x^{2}-2x$$

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

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

Evaluate

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

Solution Steps

Combine -2x and x to get -x.

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