Solve 2*25m^2div2*5m

$$2 \cdot 25 m ^ { 2 } \div 2 \cdot 5 m$$

Evaluate

$$125m^{3}$$

Solution Steps

Cancel out 2 and 2.

$$25m^{2}\times 5m$$

Multiply 25 and 5 to get 125.

$$125m^{2}m$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$125m^{3}$$

Differentiate w.r.t. m

$$375m^{2}$$

Steps Using Definition of a Derivative

Cancel out 2 and 2.

$$\frac{\mathrm{d}}{\mathrm{d}m}(25m^{2}\times 5m)$$

Multiply 25 and 5 to get 125.

$$\frac{\mathrm{d}}{\mathrm{d}m}(125m^{2}m)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}m}(125m^{3})$$

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

$$3\times 125m^{3-1}$$

Multiply 3 times 125.

$$375m^{3-1}$$

Subtract 1 from 3.

$$375m^{2}$$