Solve 7x-(-2x+1)+(-8x+1)

$$7 x - ( - 2 x + 1 ) + ( - 8 x + 1 )$$

Evaluate

$$x$$

Solution Steps

To find the opposite of -2x+1, find the opposite of each term.

$$7x-\left(-2x\right)-1-8x+1$$

The opposite of -2x is 2x.

$$7x+2x-1-8x+1$$

Combine 7x and 2x to get 9x.

$$9x-1-8x+1$$

Combine 9x and -8x to get x.

$$x-1+1$$

Add -1 and 1 to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To find the opposite of -2x+1, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x-\left(-2x\right)-1-8x+1)$$

The opposite of -2x is 2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+2x-1-8x+1)$$

Combine 7x and 2x to get 9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-1-8x+1)$$

Combine 9x and -8x to get x.

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

Add -1 and 1 to get 0.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$