Solve 5/3div25/x

$$\frac { 5 } { 3 } \div \frac { 25 } { x }$$

Evaluate

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

Solution Steps

Divide \frac{5}{3} by \frac{25}{x} by multiplying \frac{5}{3} by the reciprocal of \frac{25}{x}.

$$\frac{5x}{3\times 25}$$

Cancel out 5 in both numerator and denominator.

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

Multiply 3 and 5 to get 15.

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

Differentiate w.r.t. x

$$\frac{1}{15} = 0.06666666666666667$$

Steps Using Definition of a Derivative

Divide \frac{5}{3} by \frac{25}{x} by multiplying \frac{5}{3} by the reciprocal of \frac{25}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{3\times 25})$$

Cancel out 5 in both numerator and denominator.

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

Multiply 3 and 5 to get 15.

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

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

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

Subtract 1 from 1.

$$\frac{1}{15}x^{0}$$

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

$$\frac{1}{15}\times 1$$

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

$$\frac{1}{15}$$