Solve 1/x*6x/y

$$\frac{ 1 }{ x } \times \frac{ 6x }{ y }$$

Evaluate

$$\frac{6}{y}$$

Solution Steps

Multiply \frac{1}{x} times \frac{6x}{y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6x}{xy}$$

Cancel out x in both numerator and denominator.

$$\frac{6}{y}$$

Differentiate w.r.t. y

$$-\frac{6}{y^{2}}$$

Steps Using Definition of a Derivative

Multiply \frac{1}{x} times \frac{6x}{y} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

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

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

Subtract 1 from -1.

$$-6y^{-2}$$