Solve 1/46t+66t-7/96t

$$\frac { 1 } { 4 } 6 t + 66 t - \frac { 7 } { 9 } 6 t$$

Evaluate

$$\frac{377t}{6}$$

Solution Steps

Multiply \frac{1}{4} and 6 to get \frac{6}{4}.

$$\frac{6}{4}t+66t-\frac{7}{9}\times 6t$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}t+66t-\frac{7}{9}\times 6t$$

Combine \frac{3}{2}t and 66t to get \frac{135}{2}t.

$$\frac{135}{2}t-\frac{7}{9}\times 6t$$

Express \frac{7}{9}\times 6 as a single fraction.

$$\frac{135}{2}t-\frac{7\times 6}{9}t$$

Multiply 7 and 6 to get 42.

$$\frac{135}{2}t-\frac{42}{9}t$$

Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.

$$\frac{135}{2}t-\frac{14}{3}t$$

Combine \frac{135}{2}t and -\frac{14}{3}t to get \frac{377}{6}t.

$$\frac{377}{6}t$$

Differentiate w.r.t. t

$$\frac{377}{6} = 62\frac{5}{6} = 62.833333333333336$$

Steps Using Definition of a Derivative

Multiply \frac{1}{4} and 6 to get \frac{6}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{6}{4}t+66t-\frac{7}{9}\times 6t)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{3}{2}t+66t-\frac{7}{9}\times 6t)$$

Combine \frac{3}{2}t and 66t to get \frac{135}{2}t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{135}{2}t-\frac{7}{9}\times 6t)$$

Express \frac{7}{9}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{135}{2}t-\frac{7\times 6}{9}t)$$

Multiply 7 and 6 to get 42.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{135}{2}t-\frac{42}{9}t)$$

Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{135}{2}t-\frac{14}{3}t)$$

Combine \frac{135}{2}t and -\frac{14}{3}t to get \frac{377}{6}t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{377}{6}t)$$

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

$$\frac{377}{6}t^{1-1}$$

Subtract 1 from 1.

$$\frac{377}{6}t^{0}$$

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

$$\frac{377}{6}\times 1$$

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

$$\frac{377}{6}$$