Solve 3x/7y:x/14y^2

$$\frac { 3 x } { 7 y } : \frac { x } { 14 y ^ { 2 } }$$

Evaluate

$$6y$$

Solution Steps

Divide \frac{3x}{7y} by \frac{x}{14y^{2}} by multiplying \frac{3x}{7y} by the reciprocal of \frac{x}{14y^{2}}.

$$\frac{3x\times 14y^{2}}{7yx}$$

Cancel out 7xy in both numerator and denominator.

$$2\times 3y$$

Multiply 2 and 3 to get 6.

$$6y$$

Differentiate w.r.t. y

$$6$$

Steps Using Definition of a Derivative

Divide \frac{3x}{7y} by \frac{x}{14y^{2}} by multiplying \frac{3x}{7y} by the reciprocal of \frac{x}{14y^{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3x\times 14y^{2}}{7yx})$$

Cancel out 7xy in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2\times 3y)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y)$$

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

$$6y^{1-1}$$

Subtract 1 from 1.

$$6y^{0}$$

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

$$6\times 1$$

For any term t, t\times 1=t and 1t=t.

$$6$$