Solve =sqrt{480*240*160*80}m

$$= \sqrt { 480 \times 240 \times 160 \times 80 } m$$

Evaluate

$$38400m$$

Solution Steps

Multiply 480 and 240 to get 115200.

$$\sqrt{115200\times 160\times 80}m$$

Multiply 115200 and 160 to get 18432000.

$$\sqrt{18432000\times 80}m$$

Multiply 18432000 and 80 to get 1474560000.

$$\sqrt{1474560000}m$$

Calculate the square root of 1474560000 and get 38400.

$$38400m$$

Differentiate w.r.t. m

$$38400$$

Steps Using Definition of a Derivative

Multiply 480 and 240 to get 115200.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\sqrt{115200\times 160\times 80}m)$$

Multiply 115200 and 160 to get 18432000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\sqrt{18432000\times 80}m)$$

Multiply 18432000 and 80 to get 1474560000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\sqrt{1474560000}m)$$

Calculate the square root of 1474560000 and get 38400.

$$\frac{\mathrm{d}}{\mathrm{d}m}(38400m)$$

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

$$38400m^{1-1}$$

Subtract 1 from 1.

$$38400m^{0}$$

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

$$38400\times 1$$

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

$$38400$$