Solve 12x3*2/5

$$12x3 \times \frac{ 2 }{ 5 }$$

Evaluate

$$\frac{24x_{3}}{5}$$

Solution Steps

Express 12\times \frac{2}{5} as a single fraction.

$$\frac{12\times 2}{5}x_{3}$$

Multiply 12 and 2 to get 24.

$$\frac{24}{5}x_{3}$$

Differentiate w.r.t. x_3

$$\frac{24}{5} = 4\frac{4}{5} = 4.8$$

Steps Using Definition of a Derivative

Express 12\times \frac{2}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{12\times 2}{5}x_{3})$$

Multiply 12 and 2 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{24}{5}x_{3})$$

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

$$\frac{24}{5}x_{3}^{1-1}$$

Subtract 1 from 1.

$$\frac{24}{5}x_{3}^{0}$$

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

$$\frac{24}{5}\times 1$$

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

$$\frac{24}{5}$$