Solve (2*x)*3/4

$$(2 \times x) \times \frac{ 3 }{ 4 }$$

Evaluate

$$\frac{3x}{2}$$

Solution Steps

Express 2\times \frac{3}{4} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$\frac{6}{4}x$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}x$$

Differentiate w.r.t. x

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using Definition of a Derivative

Express 2\times \frac{3}{4} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6}{4}x)$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2}x)$$

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

$$\frac{3}{2}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{2}x^{0}$$

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

$$\frac{3}{2}\times 1$$

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

$$\frac{3}{2}$$