Solve (-1/6b-5/3b+2/3b)

$$( - \frac { 1 } { 6 } b - \frac { 5 } { 3 } b + \frac { 2 } { 3 } b )$$

Evaluate

$$-\frac{7b}{6}$$

Solution Steps

Combine -\frac{1}{6}b and -\frac{5}{3}b to get -\frac{11}{6}b.

$$-\frac{11}{6}b+\frac{2}{3}b$$

Combine -\frac{11}{6}b and \frac{2}{3}b to get -\frac{7}{6}b.

$$-\frac{7}{6}b$$

Differentiate w.r.t. b

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$

Steps Using Definition of a Derivative

Combine -\frac{1}{6}b and -\frac{5}{3}b to get -\frac{11}{6}b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-\frac{11}{6}b+\frac{2}{3}b)$$

Combine -\frac{11}{6}b and \frac{2}{3}b to get -\frac{7}{6}b.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-\frac{7}{6}b)$$

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

$$-\frac{7}{6}b^{1-1}$$

Subtract 1 from 1.

$$-\frac{7}{6}b^{0}$$

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

$$-\frac{7}{6}$$