Solve 1/3(3/4(2x))(2/5(x))

$$\frac{ 1 }{ 3 } ( \frac{ 3 }{ 4 } (2x))( \frac{ 2 }{ 5 } (x))$$

Evaluate

$$\frac{x^{2}}{5}$$

Solution Steps

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

$$\frac{1}{3}\times \frac{3}{4}\times 2x^{2}\times \frac{2}{5}$$

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{3\times 4}\times 2x^{2}\times \frac{2}{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{4}\times 2x^{2}\times \frac{2}{5}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{2}{4}x^{2}\times \frac{2}{5}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}x^{2}\times \frac{2}{5}$$

Multiply \frac{1}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{2\times 5}x^{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{5}x^{2}$$

Differentiate w.r.t. x

$$\frac{2x}{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}\times \frac{3}{4}\times 2x^{2}\times \frac{2}{5})$$

Multiply \frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 3}{3\times 4}\times 2x^{2}\times \frac{2}{5})$$

Cancel out 3 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}\times 2x^{2}\times \frac{2}{5})$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{4}x^{2}\times \frac{2}{5})$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{2}\times \frac{2}{5})$$

Multiply \frac{1}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 2}{2\times 5}x^{2})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{5}x^{2})$$

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

$$2\times \frac{1}{5}x^{2-1}$$

Multiply 2 times \frac{1}{5}.

$$\frac{2}{5}x^{2-1}$$

Subtract 1 from 2.

$$\frac{2}{5}x^{1}$$

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

$$\frac{2}{5}x$$