Solve {l}{3/4+b/15+1/2}{-5/4}

$$\left. \begin{array} { l } { \frac { 3 } { 4 } + \frac { b } { 15 } + \frac { 1 } { 2 } } \\ { - \frac { 5 } { 4 } } \end{array} \right.$$

Evaluate

$$\frac{b}{15}$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{3}{4}+\frac{b}{15}+\frac{2}{4}-\frac{5}{4}$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{4}+\frac{b}{15}-\frac{5}{4}$$

Add 3 and 2 to get 5.

$$\frac{5}{4}+\frac{b}{15}-\frac{5}{4}$$

Subtract \frac{5}{4} from \frac{5}{4} to get 0.

$$\frac{b}{15}$$

Differentiate w.r.t. b

$$\frac{1}{15} = 0.06666666666666667$$

Steps Using Definition of a Derivative

Least common multiple of 4 and 2 is 4. Convert \frac{3}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{3}{4}+\frac{b}{15}+\frac{2}{4}-\frac{5}{4})$$

Since \frac{3}{4} and \frac{2}{4} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{3+2}{4}+\frac{b}{15}-\frac{5}{4})$$

Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{5}{4}+\frac{b}{15}-\frac{5}{4})$$

Subtract \frac{5}{4} from \frac{5}{4} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{b}{15})$$

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

$$\frac{1}{15}b^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{15}b^{0}$$

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

$$\frac{1}{15}\times 1$$

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

$$\frac{1}{15}$$