Solve w^2-w+2+(-w+4)

$$w ^ { 2 } - w + 2 + ( - w + 4 )$$

Evaluate

$$w^{2}-2w+6$$

Solution Steps

Add 2 and 4 to get 6.

$$w^{2}-w+6-w$$

Combine -w and -w to get -2w.

$$w^{2}-2w+6$$

Differentiate w.r.t. w

$$2\left(w-1\right)$$

Steps Using Derivative Rule for Sum

Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}-w+6-w)$$

Combine -w and -w to get -2w.

$$\frac{\mathrm{d}}{\mathrm{d}w}(w^{2}-2w+6)$$

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}.

$$2w^{2-1}-2w^{1-1}$$

Subtract 1 from 2.

$$2w^{1}-2w^{1-1}$$

Subtract 1 from 1.

$$2w^{1}-2w^{0}$$

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

$$2w-2w^{0}$$

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

$$2w-2$$