Solve =6x^2-4x^2+2x^2-6x^2

$$= 6 x ^ { 2 } - 4 x ^ { 2 } + 2 x ^ { 2 } - 6 x ^ { 2 }$$

Evaluate

$$-2x^{2}$$

Solution Steps

Combine 6x^{2} and -4x^{2} to get 2x^{2}.

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

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$4x^{2}-6x^{2}$$

Combine 4x^{2} and -6x^{2} to get -2x^{2}.

$$-2x^{2}$$

Differentiate w.r.t. x

$$-4x$$

Steps Using Definition of a Derivative

Combine 6x^{2} and -4x^{2} to get 2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+2x^{2}-6x^{2})$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}-6x^{2})$$

Combine 4x^{2} and -6x^{2} to get -2x^{2}.

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

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

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

Multiply 2 times -2.

$$-4x^{2-1}$$

Subtract 1 from 2.

$$-4x^{1}$$

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

$$-4x$$