Solve (x*y)div(xdivz)*(xdivy)divz=

$$( x \cdot y ) \div ( x \div z ) \cdot ( x \div y ) \div z =$$

Evaluate

$$x$$

Solution Steps

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

$$\frac{\frac{xyz}{x}\times \frac{x}{y}}{z}$$

Cancel out x in both numerator and denominator.

$$\frac{yz\times \frac{x}{y}}{z}$$

Cancel out y and y.

$$\frac{xz}{z}$$

Cancel out z in both numerator and denominator.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{xyz}{x}\times \frac{x}{y}}{z})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{yz\times \frac{x}{y}}{z})$$

Cancel out y and y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xz}{z})$$

Cancel out z in both numerator and denominator.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$