Solve 10-2x-(-5x)-10+4x

$$10 - 2 x - ( - 5 x ) - 10 + 4 x$$

Evaluate

$$7x$$

Solution Steps

The opposite of -5x is 5x.

$$10-2x+5x-10+4x$$

Combine -2x and 5x to get 3x.

$$10+3x-10+4x$$

Subtract 10 from 10 to get 0.

$$3x+4x$$

Combine 3x and 4x to get 7x.

$$7x$$

Differentiate w.r.t. x

$$7$$

Steps Using Definition of a Derivative

The opposite of -5x is 5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10-2x+5x-10+4x)$$

Combine -2x and 5x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10+3x-10+4x)$$

Subtract 10 from 10 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+4x)$$

Combine 3x and 4x to get 7x.

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

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

$$7x^{1-1}$$

Subtract 1 from 1.

$$7x^{0}$$

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

$$7\times 1$$

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

$$7$$