Solve (w^2+6w-5)+(2w^2-6w-3)

$$( w ^ { 2 } + 6 w - 5 ) + ( 2 w ^ { 2 } - 6 w - 3 )$$

Evaluate

$$3w^{2}-8$$

Solution Steps

Combine w^{2} and 2w^{2} to get 3w^{2}.

$$3w^{2}+6w-5-6w-3$$

Combine 6w and -6w to get 0.

$$3w^{2}-5-3$$

Subtract 3 from -5 to get -8.

$$3w^{2}-8$$

Differentiate w.r.t. w

$$6w$$

Steps Using Derivative Rule for Sum

Combine w^{2} and 2w^{2} to get 3w^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(3w^{2}+6w-5-6w-3)$$

Combine 6w and -6w to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}w}(3w^{2}-5-3)$$

Subtract 3 from -5 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}w}(3w^{2}-8)$$

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}.

$$2\times 3w^{2-1}$$

Multiply 2 times 3.

$$6w^{2-1}$$

Subtract 1 from 2.

$$6w^{1}$$

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

$$6w$$