Solve (1.8x3/3.4)*100/180

$$\frac { ( \frac { 1.8 x 3 } { 3.4 } ) \times 100 } { 180 }$$

Evaluate

$$\frac{5x_{3}}{17}$$

Solution Steps

Divide 1.8x_{3} by 3.4 to get \frac{9}{17}x_{3}.

$$\frac{\frac{9}{17}x_{3}\times 100}{180}$$

Multiply \frac{9}{17} and 100 to get \frac{900}{17}.

$$\frac{\frac{900}{17}x_{3}}{180}$$

Divide \frac{900}{17}x_{3} by 180 to get \frac{5}{17}x_{3}.

$$\frac{5}{17}x_{3}$$

Differentiate w.r.t. x_3

$$\frac{5}{17} = 0.29411764705882354$$

Steps Using Definition of a Derivative

Divide 1.8x_{3} by 3.4 to get \frac{9}{17}x_{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{\frac{9}{17}x_{3}\times 100}{180})$$

Multiply \frac{9}{17} and 100 to get \frac{900}{17}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{\frac{900}{17}x_{3}}{180})$$

Divide \frac{900}{17}x_{3} by 180 to get \frac{5}{17}x_{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{5}{17}x_{3})$$

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

$$\frac{5}{17}x_{3}^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{17}x_{3}^{0}$$

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

$$\frac{5}{17}\times 1$$

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

$$\frac{5}{17}$$