Solve 2/5x*1/3x

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

Evaluate

$$\frac{2x^{2}}{15}$$

Solution Steps

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

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

Multiply \frac{2}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 1}{5\times 3}.

$$\frac{2}{15}x^{2}$$

Differentiate w.r.t. x

$$\frac{4x}{15}$$

Steps Using Definition of a Derivative

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

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

Multiply \frac{2}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\times 1}{5\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{15}x^{2})$$

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

$$2\times \frac{2}{15}x^{2-1}$$

Multiply 2 times \frac{2}{15}.

$$\frac{4}{15}x^{2-1}$$

Subtract 1 from 2.

$$\frac{4}{15}x^{1}$$

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

$$\frac{4}{15}x$$