Solve 2/5*5/8quadtext{(2)}7/9x

$$\frac { 2 } { 5 } \times \frac { 5 } { 8 } \quad \text { (2) } \frac { 7 } { 9 } x$$

Evaluate

$$\frac{7x}{18}$$

Solution Steps

Multiply \frac{2}{5} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 5}{5\times 8}\times 2\times \frac{7}{9}x$$

Cancel out 5 in both numerator and denominator.

$$\frac{2}{8}\times 2\times \frac{7}{9}x$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\times 2\times \frac{7}{9}x$$

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

$$\frac{2}{4}\times \frac{7}{9}x$$

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

$$\frac{1}{2}\times \frac{7}{9}x$$

Multiply \frac{1}{2} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{2\times 9}x$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 9}.

$$\frac{7}{18}x$$

Differentiate w.r.t. x

$$\frac{7}{18} = 0.3888888888888889$$

Steps Using Definition of a Derivative

Multiply \frac{2}{5} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 5}{5\times 8}\times 2\times \frac{7}{9}x)$$

Cancel out 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{8}\times 2\times \frac{7}{9}x)$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}\times 2\times \frac{7}{9}x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{4}\times \frac{7}{9}x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\times \frac{7}{9}x)$$

Multiply \frac{1}{2} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1\times 7}{2\times 9}x)$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{18}x)$$

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

$$\frac{7}{18}x^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{18}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{7}{18}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{7}{18}$$