Solve 5x3div(3+25+3*4)=

$$5 x 3 \div ( 3 + 25 + 3 \cdot 4 ) =$$

Evaluate

$$\frac{x_{3}}{8}$$

Solution Steps

Add 3 and 25 to get 28.

$$\frac{5x_{3}}{28+3\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{5x_{3}}{28+12}$$

Add 28 and 12 to get 40.

$$\frac{5x_{3}}{40}$$

Divide 5x_{3} by 40 to get \frac{1}{8}x_{3}.

$$\frac{1}{8}x_{3}$$

Differentiate w.r.t. x_3

$$\frac{1}{8} = 0.125$$

Steps Using Definition of a Derivative

Add 3 and 25 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{5x_{3}}{28+3\times 4})$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{5x_{3}}{28+12})$$

Add 28 and 12 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{5x_{3}}{40})$$

Divide 5x_{3} by 40 to get \frac{1}{8}x_{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{1}{8}x_{3})$$

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

$$\frac{1}{8}x_{3}^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{8}x_{3}^{0}$$

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

$$\frac{1}{8}\times 1$$

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

$$\frac{1}{8}$$