Solve 9/10xdiv(-3/5)

$$\frac { 9 } { 10 } x \div ( - \frac { 3 } { 5 } )$$

Evaluate

$$-\frac{3x}{2}$$

Solution Steps

Divide \frac{9}{10}x by -\frac{3}{5} by multiplying \frac{9}{10}x by the reciprocal of -\frac{3}{5}.

$$\frac{\frac{9}{10}x\times 5}{-3}$$

Express \frac{9}{10}\times 5 as a single fraction.

$$\frac{\frac{9\times 5}{10}x}{-3}$$

Multiply 9 and 5 to get 45.

$$\frac{\frac{45}{10}x}{-3}$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9}{2}x}{-3}$$

Divide \frac{9}{2}x by -3 to get -\frac{3}{2}x.

$$-\frac{3}{2}x$$

Differentiate w.r.t. x

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Definition of a Derivative

Divide \frac{9}{10}x by -\frac{3}{5} by multiplying \frac{9}{10}x by the reciprocal of -\frac{3}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{9}{10}x\times 5}{-3})$$

Express \frac{9}{10}\times 5 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{9\times 5}{10}x}{-3})$$

Multiply 9 and 5 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{45}{10}x}{-3})$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{9}{2}x}{-3})$$

Divide \frac{9}{2}x by -3 to get -\frac{3}{2}x.

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

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

$$-\frac{3}{2}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{3}{2}x^{0}$$

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

$$-\frac{3}{2}$$