Solve 4x/3y*9/2x=

$$\frac { 4 x } { 3 y } \cdot \frac { 9 } { 2 x } =$$

Evaluate

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

Solution Steps

Multiply \frac{4x}{3y} times \frac{9}{2x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x\times 9}{3y\times 2x}$$

Cancel out 2\times 3x in both numerator and denominator.

$$\frac{2\times 3}{y}$$

Multiply 2 and 3 to get 6.

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

Differentiate w.r.t. y

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

Steps Using Definition of a Derivative

Multiply \frac{4x}{3y} times \frac{9}{2x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4x\times 9}{3y\times 2x})$$

Cancel out 2\times 3x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2\times 3}{y})$$

Multiply 2 and 3 to get 6.

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

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

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

Subtract 1 from -1.

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