Solve x/12*16/100*800000

$$\frac{ x }{ 12 } \times \frac{ 16 }{ 100 } \times 800000$$

Evaluate

$$\frac{32000x}{3}$$

Solution Steps

Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{x}{12}\times \frac{4}{25}\times 800000$$

Express \frac{4}{25}\times 800000 as a single fraction.

$$\frac{x}{12}\times \frac{4\times 800000}{25}$$

Multiply 4 and 800000 to get 3200000.

$$\frac{x}{12}\times \frac{3200000}{25}$$

Divide 3200000 by 25 to get 128000.

$$\frac{x}{12}\times 128000$$

Express \frac{x}{12}\times 128000 as a single fraction.

$$\frac{x\times 128000}{12}$$

Divide x\times 128000 by 12 to get x\times \frac{32000}{3}.

$$x\times \frac{32000}{3}$$

Differentiate w.r.t. x

$$\frac{32000}{3} = 10666\frac{2}{3} = 10666.666666666666$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12}\times \frac{4}{25}\times 800000)$$

Express \frac{4}{25}\times 800000 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12}\times \frac{4\times 800000}{25})$$

Multiply 4 and 800000 to get 3200000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12}\times \frac{3200000}{25})$$

Divide 3200000 by 25 to get 128000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12}\times 128000)$$

Express \frac{x}{12}\times 128000 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 128000}{12})$$

Divide x\times 128000 by 12 to get x\times \frac{32000}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{32000}{3})$$

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

$$\frac{32000}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{32000}{3}x^{0}$$

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

$$\frac{32000}{3}\times 1$$

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

$$\frac{32000}{3}$$