Solve (-2y/1)*(-2/3)div(-9/7)

$$( - \frac { 2 y } { 1 } ) \times ( - \frac { 2 } { 3 } ) \div ( - \frac { 9 } { 7 } )$$

Evaluate

$$-\frac{28y}{27}$$

Solution Steps

Anything divided by one gives itself.

$$\frac{\left(-2y\right)\left(-\frac{2}{3}\right)}{-\frac{9}{7}}$$

Divide \left(-2y\right)\left(-\frac{2}{3}\right) by -\frac{9}{7} to get \left(-2y\right)\times \frac{14}{27}.

$$\left(-2y\right)\times \frac{14}{27}$$

Multiply -1 and 2 to get -2.

$$-2y\times \frac{14}{27}$$

Express -2\times \frac{14}{27} as a single fraction.

$$\frac{-2\times 14}{27}y$$

Multiply -2 and 14 to get -28.

$$\frac{-28}{27}y$$

Fraction \frac{-28}{27} can be rewritten as -\frac{28}{27} by extracting the negative sign.

$$-\frac{28}{27}y$$

Differentiate w.r.t. y

$$-\frac{28}{27} = -1\frac{1}{27} = -1.037037037037037$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{\left(-2y\right)\left(-\frac{2}{3}\right)}{-\frac{9}{7}})$$

Divide \left(-2y\right)\left(-\frac{2}{3}\right) by -\frac{9}{7} to get \left(-2y\right)\times \frac{14}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\left(-2y\right)\times \frac{14}{27})$$

Multiply -1 and 2 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-2y\times \frac{14}{27})$$

Express -2\times \frac{14}{27} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-2\times 14}{27}y)$$

Multiply -2 and 14 to get -28.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-28}{27}y)$$

Fraction \frac{-28}{27} can be rewritten as -\frac{28}{27} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{28}{27}y)$$

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

$$-\frac{28}{27}y^{1-1}$$

Subtract 1 from 1.

$$-\frac{28}{27}y^{0}$$

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

$$-\frac{28}{27}$$