Solve 3/2a-5/2b+1/3b+3/4a+3a+frac{13}{6}b

$$\frac { 3 } { 2 } a - \frac { 5 } { 2 } b + \frac { 1 } { 3 } b + \frac { 3 } { 4 } a + 3 a + \frac { 13 } { 6 } b$$

Evaluate

$$\frac{21a}{4}$$

Solution Steps

Combine -\frac{5}{2}b and \frac{1}{3}b to get -\frac{13}{6}b.

$$\frac{3}{2}a-\frac{13}{6}b+\frac{3}{4}a+3a+\frac{13}{6}b$$

Combine \frac{3}{2}a and \frac{3}{4}a to get \frac{9}{4}a.

$$\frac{9}{4}a-\frac{13}{6}b+3a+\frac{13}{6}b$$

Combine \frac{9}{4}a and 3a to get \frac{21}{4}a.

$$\frac{21}{4}a-\frac{13}{6}b+\frac{13}{6}b$$

Combine -\frac{13}{6}b and \frac{13}{6}b to get 0.

$$\frac{21}{4}a$$

Differentiate w.r.t. a

$$\frac{21}{4} = 5\frac{1}{4} = 5.25$$

Steps Using Definition of a Derivative

Combine -\frac{5}{2}b and \frac{1}{3}b to get -\frac{13}{6}b.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3}{2}a-\frac{13}{6}b+\frac{3}{4}a+3a+\frac{13}{6}b)$$

Combine \frac{3}{2}a and \frac{3}{4}a to get \frac{9}{4}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{9}{4}a-\frac{13}{6}b+3a+\frac{13}{6}b)$$

Combine \frac{9}{4}a and 3a to get \frac{21}{4}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{21}{4}a-\frac{13}{6}b+\frac{13}{6}b)$$

Combine -\frac{13}{6}b and \frac{13}{6}b to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{21}{4}a)$$

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

$$\frac{21}{4}a^{1-1}$$

Subtract 1 from 1.

$$\frac{21}{4}a^{0}$$

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

$$\frac{21}{4}\times 1$$

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

$$\frac{21}{4}$$