Solve 2/4*x/5

$$\frac { 2 } { 4 } \cdot \frac { x } { 5 }$$

Evaluate

$$\frac{x}{10}$$

Solution Steps

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

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

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

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

Multiply 2 and 5 to get 10.

$$\frac{x}{10}$$

Differentiate w.r.t. x

$$\frac{1}{10} = 0.1$$

Steps Using Definition of a Derivative

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

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

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

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

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{10})$$

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

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

Subtract 1 from 1.

$$\frac{1}{10}x^{0}$$

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

$$\frac{1}{10}\times 1$$

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

$$\frac{1}{10}$$