Solve {l}{x2/3}{div9/8}

$$\left. \begin{array} { l } { x \frac { 2 } { 3 } } \\ { \div \frac { 9 } { 8 } } \end{array} \right.$$

Evaluate

$$\frac{16x}{27}$$

Solution Steps

Divide x\times \frac{2}{3} by \frac{9}{8} by multiplying x\times \frac{2}{3} by the reciprocal of \frac{9}{8}.

$$\frac{x\times \frac{2}{3}\times 8}{9}$$

Express \frac{2}{3}\times 8 as a single fraction.

$$\frac{x\times \frac{2\times 8}{3}}{9}$$

Multiply 2 and 8 to get 16.

$$\frac{x\times \frac{16}{3}}{9}$$

Divide x\times \frac{16}{3} by 9 to get x\times \frac{16}{27}.

$$x\times \frac{16}{27}$$

Differentiate w.r.t. x

$$\frac{16}{27} = 0.5925925925925926$$

Steps Using Definition of a Derivative

Divide x\times \frac{2}{3} by \frac{9}{8} by multiplying x\times \frac{2}{3} by the reciprocal of \frac{9}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times \frac{2}{3}\times 8}{9})$$

Express \frac{2}{3}\times 8 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times \frac{2\times 8}{3}}{9})$$

Multiply 2 and 8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times \frac{16}{3}}{9})$$

Divide x\times \frac{16}{3} by 9 to get x\times \frac{16}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{16}{27})$$

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

$$\frac{16}{27}x^{1-1}$$

Subtract 1 from 1.

$$\frac{16}{27}x^{0}$$

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

$$\frac{16}{27}\times 1$$

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

$$\frac{16}{27}$$