Solve 3(2^4b/10)

$$3 ( \frac { 2 ^ { 4 } b } { 10 } )$$

Evaluate

$$\frac{24b}{5}$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$3\times \frac{16b}{10}$$

Divide 16b by 10 to get \frac{8}{5}b.

$$3\times \frac{8}{5}b$$

Express 3\times \frac{8}{5} as a single fraction.

$$\frac{3\times 8}{5}b$$

Multiply 3 and 8 to get 24.

$$\frac{24}{5}b$$

Differentiate w.r.t. b

$$\frac{24}{5} = 4\frac{4}{5} = 4.8$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3\times \frac{16b}{10})$$

Divide 16b by 10 to get \frac{8}{5}b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3\times \frac{8}{5}b)$$

Express 3\times \frac{8}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{3\times 8}{5}b)$$

Multiply 3 and 8 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{24}{5}b)$$

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

$$\frac{24}{5}b^{1-1}$$

Subtract 1 from 1.

$$\frac{24}{5}b^{0}$$

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

$$\frac{24}{5}\times 1$$

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

$$\frac{24}{5}$$