Solve 8xydiv(-1/2x)*(-y)

$$8 x y \div ( - \frac { 1 } { 2 } x ) \times ( - y )$$

Evaluate

$$16y^{2}$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{8y}{-\frac{1}{2}}\left(-y\right)$$

Divide 8y by -\frac{1}{2} by multiplying 8y by the reciprocal of -\frac{1}{2}.

$$\frac{8y\times 2}{-1}\left(-y\right)$$

Anything divided by -1 gives its opposite.

$$-8y\times 2\left(-y\right)$$

Multiply -8 and 2 to get -16.

$$-16y\left(-y\right)$$

Multiply -16 and -1 to get 16.

$$16yy$$

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

$$16y^{2}$$

Differentiate w.r.t. y

$$32y$$

Steps Using Definition of a Derivative

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{8y}{-\frac{1}{2}}\left(-y\right))$$

Divide 8y by -\frac{1}{2} by multiplying 8y by the reciprocal of -\frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{8y\times 2}{-1}\left(-y\right))$$

Anything divided by -1 gives its opposite.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-8y\times 2\left(-y\right))$$

Multiply -8 and 2 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-16y\left(-y\right))$$

Multiply -16 and -1 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}y}(16yy)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(16y^{2})$$

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

$$2\times 16y^{2-1}$$

Multiply 2 times 16.

$$32y^{2-1}$$

Subtract 1 from 2.

$$32y^{1}$$

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

$$32y$$