Solve 4/9*x3/4

$$\frac { 4 } { 9 } \cdot \frac { x 3 } { 4 }$$

Evaluate

$$\frac{x_{3}}{9}$$

Solution Steps

Multiply \frac{4}{9} times \frac{x_{3}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4x_{3}}{9\times 4}$$

Cancel out 4 in both numerator and denominator.

$$\frac{x_{3}}{9}$$

Differentiate w.r.t. x_3

$$\frac{1}{9} = 0.1111111111111111$$

Steps Using Definition of a Derivative

Multiply \frac{4}{9} times \frac{x_{3}}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{4x_{3}}{9\times 4})$$

Cancel out 4 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(\frac{x_{3}}{9})$$

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

$$\frac{1}{9}x_{3}^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{9}x_{3}^{0}$$

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

$$\frac{1}{9}\times 1$$

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

$$\frac{1}{9}$$