Solve m*mm*quadmm

$$m \times mm \times \quad mm$$

Evaluate

$$m^{5}$$

Solution Steps

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

$$m^{2}mmm$$

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

$$m^{3}mm$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$m^{4}m$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$m^{5}$$

Differentiate w.r.t. m

$$5m^{4}$$

Steps Using Definition of a Derivative

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{4}m)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

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

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

$$5m^{5-1}$$

Subtract 1 from 5.

$$5m^{4}$$