Solve 9x-1+3x+1+9x-1+3x+1-9x-1+3x+1

$$9x-1+3x+1+9x-1+3x+1-9x-1+3x+1$$

Evaluate

$$18x$$

Solution Steps

Combine 9x and 3x to get 12x.

$$12x-1+1+9x-1+3x+1-9x-1+3x+1$$

Add -1 and 1 to get 0.

$$12x+9x-1+3x+1-9x-1+3x+1$$

Combine 12x and 3x to get 15x.

$$15x+9x-1+1-9x-1+3x+1$$

Add -1 and 1 to get 0.

$$15x+9x-9x-1+3x+1$$

Combine 15x and 3x to get 18x.

$$18x+9x-9x-1+1$$

Add -1 and 1 to get 0.

$$18x+9x-9x$$

Combine 18x and 9x to get 27x.

$$27x-9x$$

Combine 27x and -9x to get 18x.

$$18x$$

Differentiate w.r.t. x

$$18$$

Steps Using Definition of a Derivative

Combine 9x and 3x to get 12x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x-1+1+9x-1+3x+1-9x-1+3x+1)$$

Add -1 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x+9x-1+3x+1-9x-1+3x+1)$$

Combine 12x and 3x to get 15x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x+9x-1+1-9x-1+3x+1)$$

Add -1 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x+9x-9x-1+3x+1)$$

Combine 15x and 3x to get 18x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x+9x-9x-1+1)$$

Add -1 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x+9x-9x)$$

Combine 18x and 9x to get 27x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x-9x)$$

Combine 27x and -9x to get 18x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x)$$

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

$$18x^{1-1}$$

Subtract 1 from 1.

$$18x^{0}$$

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

$$18\times 1$$

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

$$18$$