Solve 1/2x+3/2x+6x-3x=

$$\frac { 1 } { 2 } x + \frac { 3 } { 2 } x + 6 x - 3 x =$$

Evaluate

$$5x$$

Solution Steps

Combine \frac{1}{2}x and \frac{3}{2}x to get 2x.

$$2x+6x-3x$$

Combine 2x and 6x to get 8x.

$$8x-3x$$

Combine 8x and -3x to get 5x.

$$5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

Combine \frac{1}{2}x and \frac{3}{2}x to get 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x+6x-3x)$$

Combine 2x and 6x to get 8x.

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

Combine 8x and -3x to get 5x.

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

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

$$5x^{1-1}$$

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$