Solve 4x/y*5y/xz

$$\frac{ 4x }{ y } \times \frac{ 5y }{ xz }$$

Evaluate

$$\frac{20}{z}$$

Solution Steps

Multiply \frac{4x}{y} times \frac{5y}{xz} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x\times 5y}{yxz}$$

Cancel out xy in both numerator and denominator.

$$\frac{4\times 5}{z}$$

Multiply 4 and 5 to get 20.

$$\frac{20}{z}$$

Differentiate w.r.t. z

$$-\frac{20}{z^{2}}$$

Steps Using Definition of a Derivative

Multiply \frac{4x}{y} times \frac{5y}{xz} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{4x\times 5y}{yxz})$$

Cancel out xy in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{4\times 5}{z})$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{20}{z})$$

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

$$-20z^{-1-1}$$

Subtract 1 from -1.

$$-20z^{-2}$$