Solve 2*(2/3mm*5/6m^2)

$$2 \cdot ( \frac { 2 } { 3 } m m \cdot \frac { 5 } { 6 } m ^ { 2 } )$$

Evaluate

$$\frac{10m^{4}}{9}$$

Solution Steps

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

$$2\times \frac{2}{3}m^{2}\times \frac{5}{6}m^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2\times \frac{2}{3}m^{4}\times \frac{5}{6}$$

Multiply 2 and \frac{2}{3} to get \frac{4}{3}.

$$\frac{4}{3}m^{4}\times \frac{5}{6}$$

Multiply \frac{4}{3} and \frac{5}{6} to get \frac{10}{9}.

$$\frac{10}{9}m^{4}$$

Differentiate w.r.t. m

$$\frac{40m^{3}}{9}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(2\times \frac{2}{3}m^{2}\times \frac{5}{6}m^{2})$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}m}(2\times \frac{2}{3}m^{4}\times \frac{5}{6})$$

Multiply 2 and \frac{2}{3} to get \frac{4}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{4}{3}m^{4}\times \frac{5}{6})$$

Multiply \frac{4}{3} and \frac{5}{6} to get \frac{10}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{10}{9}m^{4})$$

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

$$4\times \frac{10}{9}m^{4-1}$$

Multiply 4 times \frac{10}{9}.

$$\frac{40}{9}m^{4-1}$$

Subtract 1 from 4.

$$\frac{40}{9}m^{3}$$