Solve 27-b+8b+3b-8

$$27 - b + 8 b + 3 b - 8$$

Evaluate

$$10b+19$$

Solution Steps

Combine -b and 8b to get 7b.

$$27+7b+3b-8$$

Combine 7b and 3b to get 10b.

$$27+10b-8$$

Subtract 8 from 27 to get 19.

$$19+10b$$

Differentiate w.r.t. b

$$10$$

Steps Using Derivative Rule for Sum

Combine -b and 8b to get 7b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(27+7b+3b-8)$$

Combine 7b and 3b to get 10b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(27+10b-8)$$

Subtract 8 from 27 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}b}(19+10b)$$

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}.

$$10b^{1-1}$$

Subtract 1 from 1.

$$10b^{0}$$

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

$$10\times 1$$

For any term t, t\times 1=t and 1t=t.

$$10$$