Solve 3x-2x+7x=

$$3 x - 2 x + 7 x =$$

Evaluate

$$8x$$

Solution Steps

Combine 3x and -2x to get x.

$$x+7x$$

Combine x and 7x to get 8x.

$$8x$$

Differentiate w.r.t. x

$$8$$

Steps Using Definition of a Derivative

Combine 3x and -2x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+7x)$$

Combine x and 7x to get 8x.

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

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

$$8x^{1-1}$$

Subtract 1 from 1.

$$8x^{0}$$

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

$$8\times 1$$

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

$$8$$