Solve 7/30t-45/15t+9/30t

$$\frac { 7 } { 30 } t - \frac { 45 } { 15 } t + \frac { 9 } { 30 } t$$

Evaluate

$$-\frac{37t}{15}$$

Solution Steps

Divide 45 by 15 to get 3.

$$\frac{7}{30}t-3t+\frac{9}{30}t$$

Combine \frac{7}{30}t and -3t to get -\frac{83}{30}t.

$$-\frac{83}{30}t+\frac{9}{30}t$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$-\frac{83}{30}t+\frac{3}{10}t$$

Combine -\frac{83}{30}t and \frac{3}{10}t to get -\frac{37}{15}t.

$$-\frac{37}{15}t$$

Differentiate w.r.t. t

$$-\frac{37}{15} = -2\frac{7}{15} = -2.466666666666667$$

Steps Using Definition of a Derivative

Divide 45 by 15 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{7}{30}t-3t+\frac{9}{30}t)$$

Combine \frac{7}{30}t and -3t to get -\frac{83}{30}t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-\frac{83}{30}t+\frac{9}{30}t)$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-\frac{83}{30}t+\frac{3}{10}t)$$

Combine -\frac{83}{30}t and \frac{3}{10}t to get -\frac{37}{15}t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(-\frac{37}{15}t)$$

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

$$-\frac{37}{15}t^{1-1}$$

Subtract 1 from 1.

$$-\frac{37}{15}t^{0}$$

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

$$-\frac{37}{15}$$