Solve 1*(10/3x)div(5/6x)

$$1 \cdot ( \frac { 10 } { 3 } x ) \div ( \frac { 5 } { 6 x } )$$

Evaluate

$$4x^{2}$$

Solution Steps

Multiply 1 and \frac{10}{3} to get \frac{10}{3}.

$$\frac{\frac{10}{3}x}{\frac{5}{6x}}$$

Divide \frac{10}{3}x by \frac{5}{6x} by multiplying \frac{10}{3}x by the reciprocal of \frac{5}{6x}.

$$\frac{\frac{10}{3}x\times 6x}{5}$$

Multiply x and x to get x^{2}.

$$\frac{\frac{10}{3}x^{2}\times 6}{5}$$

Express \frac{10}{3}\times 6 as a single fraction.

$$\frac{\frac{10\times 6}{3}x^{2}}{5}$$

Multiply 10 and 6 to get 60.

$$\frac{\frac{60}{3}x^{2}}{5}$$

Divide 60 by 3 to get 20.

$$\frac{20x^{2}}{5}$$

Divide 20x^{2} by 5 to get 4x^{2}.

$$4x^{2}$$

Differentiate w.r.t. x

$$8x$$

Steps Using Definition of a Derivative

Multiply 1 and \frac{10}{3} to get \frac{10}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{10}{3}x}{\frac{5}{6x}})$$

Divide \frac{10}{3}x by \frac{5}{6x} by multiplying \frac{10}{3}x by the reciprocal of \frac{5}{6x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{10}{3}x\times 6x}{5})$$

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{10}{3}x^{2}\times 6}{5})$$

Express \frac{10}{3}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{10\times 6}{3}x^{2}}{5})$$

Multiply 10 and 6 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{60}{3}x^{2}}{5})$$

Divide 60 by 3 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20x^{2}}{5})$$

Divide 20x^{2} by 5 to get 4x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2})$$

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

$$2\times 4x^{2-1}$$

Multiply 2 times 4.

$$8x^{2-1}$$

Subtract 1 from 2.

$$8x^{1}$$

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

$$8x$$