Solve 4/5*x/100

$$\frac { 4 } { 5 } \times \frac { x } { 100 }$$

Evaluate

$$\frac{x}{125}$$

Solution Steps

Multiply \frac{4}{5} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x}{5\times 100}$$

Cancel out 4 in both numerator and denominator.

$$\frac{x}{5\times 25}$$

Multiply 5 and 25 to get 125.

$$\frac{x}{125}$$

Differentiate w.r.t. x

$$\frac{1}{125} = 0.008$$

Steps Using Definition of a Derivative

Multiply \frac{4}{5} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x}{5\times 100})$$

Cancel out 4 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5\times 25})$$

Multiply 5 and 25 to get 125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{125})$$

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

$$\frac{1}{125}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{125}x^{0}$$

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

$$\frac{1}{125}\times 1$$

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

$$\frac{1}{125}$$