Solve 5x/1x*4/5y

$$\frac{ 5x }{ 1x } \times \frac{ 4 }{ 5y }$$

Evaluate

$$\frac{4}{y}$$

Solution Steps

Cancel out x in both numerator and denominator.

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

Express 5\times \frac{4}{5y} as a single fraction.

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

Cancel out 5 in both numerator and denominator.

$$\frac{4}{y}$$

Differentiate w.r.t. y

$$-\frac{4}{y^{2}}$$

Steps Using Definition of a Derivative

Cancel out x in both numerator and denominator.

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

Express 5\times \frac{4}{5y} as a single fraction.

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

Cancel out 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4}{y})$$

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

$$-4y^{-1-1}$$

Subtract 1 from -1.

$$-4y^{-2}$$