Solve 4/43x1/2

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

Evaluate

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

Solution Steps

Divide 4 by 4 to get 1.

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

Multiply 1 and 3 to get 3.

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

Multiply 3 and \frac{1}{2} to get \frac{3}{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

Divide 4 by 4 to get 1.

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

Multiply 1 and 3 to get 3.

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

Multiply 3 and \frac{1}{2} to get \frac{3}{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.

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