Solve ((3x)div8)*6

$$((3x) \div 8) \times 6$$

Evaluate

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

Solution Steps

Express \frac{3x}{8}\times 6 as a single fraction.

$$\frac{3x\times 6}{8}$$

Multiply 3 and 6 to get 18.

$$\frac{18x}{8}$$

Divide 18x by 8 to get \frac{9}{4}x.

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

Differentiate w.r.t. x

$$\frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps Using Definition of a Derivative

Express \frac{3x}{8}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x\times 6}{8})$$

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x}{8})$$

Divide 18x by 8 to get \frac{9}{4}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{4}x)$$

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

$$\frac{9}{4}x^{1-1}$$

Subtract 1 from 1.

$$\frac{9}{4}x^{0}$$

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

$$\frac{9}{4}\times 1$$

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

$$\frac{9}{4}$$