Solve x:0,04div24:0,4

$$x : 0,04 \div 24 : 0,4$$

Evaluate

$$\frac{125x}{48}$$

Solution Steps

Express \frac{\frac{\frac{x}{0,04}}{24}}{0,4} as a single fraction.

$$\frac{\frac{x}{0,04}}{24\times 0,4}$$

Multiply 24 and 0,4 to get 9,6.

$$\frac{\frac{x}{0,04}}{9,6}$$

Express \frac{\frac{x}{0,04}}{9,6} as a single fraction.

$$\frac{x}{0,04\times 9,6}$$

Multiply 0,04 and 9,6 to get 0,384.

$$\frac{x}{0,384}$$

Differentiate w.r.t. x

$$\frac{125}{48} = 2\frac{29}{48} = 2.6041666666666665$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{x}{0,04}}{24}}{0,4} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{0,04}}{24\times 0,4})$$

Multiply 24 and 0,4 to get 9,6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{0,04}}{9,6})$$

Express \frac{\frac{x}{0,04}}{9,6} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{0,04\times 9,6})$$

Multiply 0,04 and 9,6 to get 0,384.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{0,384})$$

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

$$\frac{125}{48}x^{1-1}$$

Subtract 1 from 1.

$$\frac{125}{48}x^{0}$$

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

$$\frac{125}{48}\times 1$$

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

$$\frac{125}{48}$$