Solve 1/2x*2+1/2x*10

$$\frac{ 1 }{ 2 } x \times 2+ \frac{ 1 }{ 2 } x \times 10$$

Evaluate

$$6x$$

Solution Steps

Cancel out 2 and 2.

$$x+\frac{1}{2}x\times 10$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$x+\frac{10}{2}x$$

Divide 10 by 2 to get 5.

$$x+5x$$

Combine x and 5x to get 6x.

$$6x$$

Differentiate w.r.t. x

$$6$$

Steps Using Definition of a Derivative

Cancel out 2 and 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{1}{2}x\times 10)$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{10}{2}x)$$

Divide 10 by 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+5x)$$

Combine x and 5x to get 6x.

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

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

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$