Solve x/1/2*10/3/2=

$$\frac { x } { 1 / 2 } \times \frac { 10 } { 3 / 2 } =$$

Evaluate

$$\frac{40x}{3}$$

Solution Steps

Divide x by \frac{1}{2} by multiplying x by the reciprocal of \frac{1}{2}.

$$x\times 2\times \frac{10}{\frac{3}{2}}$$

Divide 10 by \frac{3}{2} by multiplying 10 by the reciprocal of \frac{3}{2}.

$$x\times 2\times 10\times \frac{2}{3}$$

Express 10\times \frac{2}{3} as a single fraction.

$$x\times 2\times \frac{10\times 2}{3}$$

Multiply 10 and 2 to get 20.

$$x\times 2\times \frac{20}{3}$$

Express 2\times \frac{20}{3} as a single fraction.

$$x\times \frac{2\times 20}{3}$$

Multiply 2 and 20 to get 40.

$$x\times \frac{40}{3}$$

Differentiate w.r.t. x

$$\frac{40}{3} = 13\frac{1}{3} = 13.333333333333334$$

Steps Using Definition of a Derivative

Divide x by \frac{1}{2} by multiplying x by the reciprocal of \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 2\times \frac{10}{\frac{3}{2}})$$

Divide 10 by \frac{3}{2} by multiplying 10 by the reciprocal of \frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 2\times 10\times \frac{2}{3})$$

Express 10\times \frac{2}{3} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 2\times \frac{10\times 2}{3})$$

Multiply 10 and 2 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 2\times \frac{20}{3})$$

Express 2\times \frac{20}{3} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{2\times 20}{3})$$

Multiply 2 and 20 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{40}{3})$$

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

$$\frac{40}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{40}{3}x^{0}$$

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

$$\frac{40}{3}\times 1$$

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

$$\frac{40}{3}$$