Solve 8x^2-x^2-12x^2+2x^2

$$8 x ^ { 2 } - x ^ { 2 } - 12 x ^ { 2 } + 2 x ^ { 2 }$$

Evaluate

$$-3x^{2}$$

Solution Steps

Combine 8x^{2} and -x^{2} to get 7x^{2}.

$$7x^{2}-12x^{2}+2x^{2}$$

Combine 7x^{2} and -12x^{2} to get -5x^{2}.

$$-5x^{2}+2x^{2}$$

Combine -5x^{2} and 2x^{2} to get -3x^{2}.

$$-3x^{2}$$

Differentiate w.r.t. x

$$-6x$$

Steps Using Definition of a Derivative

Combine 8x^{2} and -x^{2} to get 7x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}-12x^{2}+2x^{2})$$

Combine 7x^{2} and -12x^{2} to get -5x^{2}.

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

Combine -5x^{2} and 2x^{2} to get -3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{2})$$

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

$$2\left(-3\right)x^{2-1}$$

Multiply 2 times -3.

$$-6x^{2-1}$$

Subtract 1 from 2.

$$-6x^{1}$$

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

$$-6x$$