Solve x/12div5x+x/18div5x

$$\frac { x } { 12 } \div 5 x + \frac { x } { 18 } \div 5 x$$

Evaluate

$$\frac{x^{2}}{36}$$

Solution Steps

Express \frac{\frac{x}{12}}{5} as a single fraction.

$$\frac{x}{12\times 5}x+\frac{\frac{x}{18}}{5}x$$

Multiply 12 and 5 to get 60.

$$\frac{x}{60}x+\frac{\frac{x}{18}}{5}x$$

Express \frac{x}{60}x as a single fraction.

$$\frac{xx}{60}+\frac{\frac{x}{18}}{5}x$$

Express \frac{\frac{x}{18}}{5} as a single fraction.

$$\frac{xx}{60}+\frac{x}{18\times 5}x$$

Multiply 18 and 5 to get 90.

$$\frac{xx}{60}+\frac{x}{90}x$$

Express \frac{x}{90}x as a single fraction.

$$\frac{xx}{60}+\frac{xx}{90}$$

Combine \frac{xx}{60} and \frac{xx}{90} to get \frac{1}{36}xx.

$$\frac{1}{36}xx$$

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

$$\frac{1}{36}x^{2}$$

Differentiate w.r.t. x

$$\frac{x}{18}$$

Steps Using Definition of a Derivative

Express \frac{\frac{x}{12}}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12\times 5}x+\frac{\frac{x}{18}}{5}x)$$

Multiply 12 and 5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{60}x+\frac{\frac{x}{18}}{5}x)$$

Express \frac{x}{60}x as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{60}+\frac{\frac{x}{18}}{5}x)$$

Express \frac{\frac{x}{18}}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{60}+\frac{x}{18\times 5}x)$$

Multiply 18 and 5 to get 90.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{60}+\frac{x}{90}x)$$

Express \frac{x}{90}x as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx}{60}+\frac{xx}{90})$$

Combine \frac{xx}{60} and \frac{xx}{90} to get \frac{1}{36}xx.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{36}xx)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{36}x^{2})$$

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

$$2\times \frac{1}{36}x^{2-1}$$

Multiply 2 times \frac{1}{36}.

$$\frac{1}{18}x^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{18}x^{1}$$

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

$$\frac{1}{18}x$$