Solve (1/2x^2-3x+41/2)^prime=

$$( \frac { 1 } { 2 } x ^ { 2 } - 3 x + 4 \frac { 1 } { 2 } ) ^ { \prime } =$$

Evaluate

$$x-3$$

Steps Using Derivative Rule for Sum

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}-3x+\frac{8+1}{2})$$

Add 8 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}-3x+\frac{9}{2})$$

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}.

$$2\times \frac{1}{2}x^{2-1}-3x^{1-1}$$

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

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

$$x-3$$

Differentiate w.r.t. x

$$1$$