Solve -3x^2ydiv3x^2/4y

$$- 3 x ^ { 2 } y \div \frac { 3 x ^ { 2 } } { 4 y }$$

Evaluate

$$-4y^{2}$$

Solution Steps

Divide -3x^{2}y by \frac{3x^{2}}{4y} by multiplying -3x^{2}y by the reciprocal of \frac{3x^{2}}{4y}.

$$\frac{-3x^{2}y\times 4y}{3x^{2}}$$

Cancel out 3x^{2} in both numerator and denominator.

$$-4yy$$

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

$$-4y^{2}$$

Differentiate w.r.t. y

$$-8y$$

Steps Using Definition of a Derivative

Divide -3x^{2}y by \frac{3x^{2}}{4y} by multiplying -3x^{2}y by the reciprocal of \frac{3x^{2}}{4y}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-3x^{2}y\times 4y}{3x^{2}})$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-4yy)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(-4y^{2})$$

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

$$2\left(-4\right)y^{2-1}$$

Multiply 2 times -4.

$$-8y^{2-1}$$

Subtract 1 from 2.

$$-8y^{1}$$

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

$$-8y$$