Solve 2/3x1/5x3/4=

$$\frac { 2 } { 3 } x \frac { 1 } { 5 } x \frac { 3 } { 4 } =$$

Evaluate

$$\frac{x^{2}}{10}$$

Solution Steps

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

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

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

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

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

$$\frac{2}{15}x^{2}\times \frac{3}{4}$$

Multiply \frac{2}{15} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3}{15\times 4}x^{2}$$

Do the multiplications in the fraction \frac{2\times 3}{15\times 4}.

$$\frac{6}{60}x^{2}$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$\frac{1}{10}x^{2}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{15}x^{2}\times \frac{3}{4})$$

Multiply \frac{2}{15} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 3}{15\times 4}x^{2})$$

Do the multiplications in the fraction \frac{2\times 3}{15\times 4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{60}x^{2})$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{10}x^{2})$$

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

$$2\times \frac{1}{10}x^{2-1}$$

Multiply 2 times \frac{1}{10}.

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

Subtract 1 from 2.

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

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

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