Solve 5x+7x-x+3x-21x

$$5 x + 7 x - x + 3 x - 21 x$$

Evaluate

$$-7x$$

Solution Steps

Combine 5x and 7x to get 12x.

$$12x-x+3x-21x$$

Combine 12x and -x to get 11x.

$$11x+3x-21x$$

Combine 11x and 3x to get 14x.

$$14x-21x$$

Combine 14x and -21x to get -7x.

$$-7x$$

Differentiate w.r.t. x

$$-7$$

Steps Using Definition of a Derivative

Combine 5x and 7x to get 12x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x-x+3x-21x)$$

Combine 12x and -x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x+3x-21x)$$

Combine 11x and 3x to get 14x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(14x-21x)$$

Combine 14x and -21x 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.

$$-7$$