Solve 2(3/5m)(5/3)

$$2 ( \frac { 3 } { 5 } m ) ( \frac { 5 } { 3 } )$$

Evaluate

$$2m$$

Solution Steps

Express 2\times \frac{3}{5} as a single fraction.

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

Multiply 2 and 3 to get 6.

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

Multiply \frac{6}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

$$\frac{6}{3}m$$

Divide 6 by 3 to get 2.

$$2m$$

Differentiate w.r.t. m

$$2$$

Steps Using Definition of a Derivative

Express 2\times \frac{3}{5} as a single fraction.

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

Multiply 2 and 3 to get 6.

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

Multiply \frac{6}{5} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{6}{3}m)$$

Divide 6 by 3 to get 2.

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

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

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

Subtract 1 from 1.

$$2m^{0}$$

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

$$2\times 1$$

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

$$2$$