Solve 22/21a^2div(2a/5+a)

$$\frac { 22 } { 21 } a ^ { 2 } \div ( \frac { 2 a } { 5 } + a )$$

Evaluate

$$\frac{110a}{147}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{5}{5}.

$$\frac{\frac{22}{21}a^{2}}{\frac{2a}{5}+\frac{5a}{5}}$$

Since \frac{2a}{5} and \frac{5a}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{22}{21}a^{2}}{\frac{2a+5a}{5}}$$

Combine like terms in 2a+5a.

$$\frac{\frac{22}{21}a^{2}}{\frac{7a}{5}}$$

Divide \frac{22}{21}a^{2} by \frac{7a}{5} by multiplying \frac{22}{21}a^{2} by the reciprocal of \frac{7a}{5}.

$$\frac{\frac{22}{21}a^{2}\times 5}{7a}$$

Cancel out a in both numerator and denominator.

$$\frac{\frac{22}{21}\times 5a}{7}$$

Multiply \frac{22}{21} and 5 to get \frac{110}{21}.

$$\frac{\frac{110}{21}a}{7}$$

Divide \frac{110}{21}a by 7 to get \frac{110}{147}a.

$$\frac{110}{147}a$$

Differentiate w.r.t. a

$$\frac{110}{147} = 0.7482993197278912$$

Steps Using Definition of a Derivative

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{5}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{22}{21}a^{2}}{\frac{2a}{5}+\frac{5a}{5}})$$

Since \frac{2a}{5} and \frac{5a}{5} have the same denominator, add them by adding their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{22}{21}a^{2}}{\frac{2a+5a}{5}})$$

Combine like terms in 2a+5a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{22}{21}a^{2}}{\frac{7a}{5}})$$

Divide \frac{22}{21}a^{2} by \frac{7a}{5} by multiplying \frac{22}{21}a^{2} by the reciprocal of \frac{7a}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{22}{21}a^{2}\times 5}{7a})$$

Cancel out a in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{22}{21}\times 5a}{7})$$

Multiply \frac{22}{21} and 5 to get \frac{110}{21}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{110}{21}a}{7})$$

Divide \frac{110}{21}a by 7 to get \frac{110}{147}a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{110}{147}a)$$

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

$$\frac{110}{147}a^{1-1}$$

Subtract 1 from 1.

$$\frac{110}{147}a^{0}$$

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

$$\frac{110}{147}\times 1$$

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

$$\frac{110}{147}$$