Solve (1/3x^3-1/2x^2+x)^prime

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

Evaluate

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

Steps Using Derivative Rule for Sum

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}.

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

Multiply 3 times \frac{1}{3}.

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

Subtract 1 from 3.

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

Multiply 2 times -\frac{1}{2}.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

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

Differentiate w.r.t. x

$$2x-1$$