Solve 5/7m+3/4m-5/8m

$$\frac { 5 } { 7 } m + \frac { 3 } { 4 } m - \frac { 5 } { 8 } m$$

Evaluate

$$\frac{47m}{56}$$

Solution Steps

Combine \frac{5}{7}m and \frac{3}{4}m to get \frac{41}{28}m.

$$\frac{41}{28}m-\frac{5}{8}m$$

Combine \frac{41}{28}m and -\frac{5}{8}m to get \frac{47}{56}m.

$$\frac{47}{56}m$$

Differentiate w.r.t. m

$$\frac{47}{56} = 0.8392857142857143$$

Steps Using Definition of a Derivative

Combine \frac{5}{7}m and \frac{3}{4}m to get \frac{41}{28}m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{41}{28}m-\frac{5}{8}m)$$

Combine \frac{41}{28}m and -\frac{5}{8}m to get \frac{47}{56}m.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{47}{56}m)$$

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

$$\frac{47}{56}m^{1-1}$$

Subtract 1 from 1.

$$\frac{47}{56}m^{0}$$

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

$$\frac{47}{56}\times 1$$

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

$$\frac{47}{56}$$