Solve b+3b+5b+7b

$$b + 3 b + 5 b + 7 b$$

Evaluate

$$16b$$

Solution Steps

Combine b and 3b to get 4b.

$$4b+5b+7b$$

Combine 4b and 5b to get 9b.

$$9b+7b$$

Combine 9b and 7b to get 16b.

$$16b$$

Differentiate w.r.t. b

$$16$$

Steps Using Definition of a Derivative

Combine b and 3b to get 4b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b+5b+7b)$$

Combine 4b and 5b to get 9b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(9b+7b)$$

Combine 9b and 7b to get 16b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(16b)$$

The derivative of ax^{n} is nax^{n-1}.

$$16b^{1-1}$$

Subtract 1 from 1.

$$16b^{0}$$

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

$$16\times 1$$

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

$$16$$