Solve 3x/4*2x/9

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

Evaluate

$$\frac{x^{2}}{6}$$

Solution Steps

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

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

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

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

Multiply x and x to get x^{2}.

$$\frac{x^{2}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{x^{2}}{6}$$

Differentiate w.r.t. x

$$\frac{x}{3}$$

Steps Using Definition of a Derivative

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

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

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

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

Multiply x and x to get x^{2}.

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

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{6})$$

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

$$2\times \frac{1}{6}x^{2-1}$$

Multiply 2 times \frac{1}{6}.

$$\frac{1}{3}x^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{3}x^{1}$$

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

$$\frac{1}{3}x$$