Solve 81340x10/100x100/90

$$81340x \frac{ 10 }{ 100 } x \frac{ 100 }{ 90 }$$

Evaluate

$$\frac{81340x^{2}}{9}$$

Solution Steps

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

$$81340x^{2}\times \frac{10}{100}\times \frac{100}{90}$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$81340x^{2}\times \frac{1}{10}\times \frac{100}{90}$$

Multiply 81340 and \frac{1}{10} to get \frac{81340}{10}.

$$\frac{81340}{10}x^{2}\times \frac{100}{90}$$

Divide 81340 by 10 to get 8134.

$$8134x^{2}\times \frac{100}{90}$$

Reduce the fraction \frac{100}{90} to lowest terms by extracting and canceling out 10.

$$8134x^{2}\times \frac{10}{9}$$

Express 8134\times \frac{10}{9} as a single fraction.

$$\frac{8134\times 10}{9}x^{2}$$

Multiply 8134 and 10 to get 81340.

$$\frac{81340}{9}x^{2}$$

Differentiate w.r.t. x

$$\frac{162680x}{9}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(81340x^{2}\times \frac{10}{100}\times \frac{100}{90})$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(81340x^{2}\times \frac{1}{10}\times \frac{100}{90})$$

Multiply 81340 and \frac{1}{10} to get \frac{81340}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{81340}{10}x^{2}\times \frac{100}{90})$$

Divide 81340 by 10 to get 8134.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8134x^{2}\times \frac{100}{90})$$

Reduce the fraction \frac{100}{90} to lowest terms by extracting and canceling out 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8134x^{2}\times \frac{10}{9})$$

Express 8134\times \frac{10}{9} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8134\times 10}{9}x^{2})$$

Multiply 8134 and 10 to get 81340.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{81340}{9}x^{2})$$

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

$$2\times \frac{81340}{9}x^{2-1}$$

Multiply 2 times \frac{81340}{9}.

$$\frac{162680}{9}x^{2-1}$$

Subtract 1 from 2.

$$\frac{162680}{9}x^{1}$$

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

$$\frac{162680}{9}x$$