Solve x:0,04:24:04

$$x : 0,04 : 24 : 04$$

Evaluate

$$\frac{25x}{96}$$

Solution Steps

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

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

Multiply 24 and 4 to get 96.

$$\frac{\frac{x}{0,04}}{96}$$

Express \frac{\frac{x}{0,04}}{96} as a single fraction.

$$\frac{x}{0,04\times 96}$$

Multiply 0,04 and 96 to get 3,84.

$$\frac{x}{3,84}$$

Differentiate w.r.t. x

$$\frac{25}{96} = 0.2604166666666667$$

Steps Using Definition of a Derivative

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

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

Multiply 24 and 4 to get 96.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{0,04}}{96})$$

Express \frac{\frac{x}{0,04}}{96} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{0,04\times 96})$$

Multiply 0,04 and 96 to get 3,84.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{3,84})$$

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

$$\frac{25}{96}x^{1-1}$$

Subtract 1 from 1.

$$\frac{25}{96}x^{0}$$

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

$$\frac{25}{96}\times 1$$

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

$$\frac{25}{96}$$