Solve 400m:1*5m

$$400 m : 1 \cdot 5 m$$

Evaluate

$$2000m^{2}$$

Solution Steps

Anything divided by one gives itself.

$$400m\times 5m$$

Multiply 400 and 5 to get 2000.

$$2000mm$$

Multiply m and m to get m^{2}.

$$2000m^{2}$$

Differentiate w.r.t. m

$$4000m$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}m}(400m\times 5m)$$

Multiply 400 and 5 to get 2000.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2000mm)$$

Multiply m and m to get m^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2000m^{2})$$

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

$$2\times 2000m^{2-1}$$

Multiply 2 times 2000.

$$4000m^{2-1}$$

Subtract 1 from 2.

$$4000m^{1}$$

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

$$4000m$$