Solve 3x^2/4div(9x)

$$\frac { 3 x ^ { 2 } } { 4 } \div ( 9 x )$$

Evaluate

$$\frac{x}{12}$$

Solution Steps

Express \frac{\frac{3x^{2}}{4}}{9x} as a single fraction.

$$\frac{3x^{2}}{4\times 9x}$$

Cancel out 3x in both numerator and denominator.

$$\frac{x}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{x}{12}$$

Differentiate w.r.t. x

$$\frac{1}{12} = 0.08333333333333333$$

Steps Using Definition of a Derivative

Express \frac{\frac{3x^{2}}{4}}{9x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{2}}{4\times 9x})$$

Cancel out 3x in both numerator and denominator.

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

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{12})$$

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

$$\frac{1}{12}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{12}x^{0}$$

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

$$\frac{1}{12}\times 1$$

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

$$\frac{1}{12}$$