Solve 8/3quadtext{(b)}9

$$8 / 3 \quad \text { (b) } 9$$

Evaluate

$$24b$$

Solution Steps

Express \frac{8}{3}\times 9 as a single fraction.

$$\frac{8\times 9}{3}b$$

Multiply 8 and 9 to get 72.

$$\frac{72}{3}b$$

Divide 72 by 3 to get 24.

$$24b$$

Differentiate w.r.t. b

$$24$$

Steps Using Definition of a Derivative

Express \frac{8}{3}\times 9 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{8\times 9}{3}b)$$

Multiply 8 and 9 to get 72.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{72}{3}b)$$

Divide 72 by 3 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}b}(24b)$$

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

$$24b^{1-1}$$

Subtract 1 from 1.

$$24b^{0}$$

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

$$24\times 1$$

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

$$24$$