Solve x/frac{x{Y}}

$$\frac { x } { \frac { x } { Y } }$$

Evaluate

$$Y$$

Solution Steps

Divide x by \frac{x}{Y} by multiplying x by the reciprocal of \frac{x}{Y}.

$$\frac{xY}{x}$$

Cancel out x in both numerator and denominator.

$$Y$$

Differentiate w.r.t. Y

$$1$$

Steps Using Definition of a Derivative

Divide x by \frac{x}{Y} by multiplying x by the reciprocal of \frac{x}{Y}.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(\frac{xY}{x})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}Y}(Y)$$

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

$$Y^{1-1}$$

Subtract 1 from 1.

$$Y^{0}$$

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

$$1$$