Solve 58-(+5b)-(-13)+(+28b)-17

$$58 - ( + 5 b ) - ( - 13 ) + ( + 28 b ) - 17$$

Evaluate

$$23b+54$$

Solution Steps

The opposite of -13 is 13.

$$58-5b+13+28b-17$$

Add 58 and 13 to get 71.

$$71-5b+28b-17$$

Combine -5b and 28b to get 23b.

$$71+23b-17$$

Subtract 17 from 71 to get 54.

$$54+23b$$

Differentiate w.r.t. b

$$23$$

Steps Using Derivative Rule for Sum

The opposite of -13 is 13.

$$\frac{\mathrm{d}}{\mathrm{d}b}(58-5b+13+28b-17)$$

Add 58 and 13 to get 71.

$$\frac{\mathrm{d}}{\mathrm{d}b}(71-5b+28b-17)$$

Combine -5b and 28b to get 23b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(71+23b-17)$$

Subtract 17 from 71 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}b}(54+23b)$$

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}.

$$23b^{1-1}$$

Subtract 1 from 1.

$$23b^{0}$$

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

$$23\times 1$$

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

$$23$$