Solve 2(4/8x)(3/4)

$$2 ( \frac { 4 } { 8 } x ) ( \frac { 3 } { 4 } )$$

Evaluate

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

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$2\times \frac{1}{2}x\times \frac{3}{4}$$

Cancel out 2 and 2.

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

Differentiate w.r.t. x

$$\frac{3}{4} = 0.75$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\times \frac{1}{2}x\times \frac{3}{4})$$

Cancel out 2 and 2.

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

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

$$\frac{3}{4}x^{1-1}$$

Subtract 1 from 1.

$$\frac{3}{4}x^{0}$$

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

$$\frac{3}{4}\times 1$$

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

$$\frac{3}{4}$$