Solve 2x^2-6x^2+8x-18x+10x

$$2 x ^ { 2 } - 6 x ^ { 2 } + 8 x - 18 x + 10 x$$

Evaluate

$$-4x^{2}$$

Solution Steps

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

$$-4x^{2}+8x-18x+10x$$

Combine 8x and -18x to get -10x.

$$-4x^{2}-10x+10x$$

Combine -10x and 10x to get 0.

$$-4x^{2}$$

Differentiate w.r.t. x

$$-8x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{2}+8x-18x+10x)$$

Combine 8x and -18x to get -10x.

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

Combine -10x and 10x to get 0.

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

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

$$2\left(-4\right)x^{2-1}$$

Multiply 2 times -4.

$$-8x^{2-1}$$

Subtract 1 from 2.

$$-8x^{1}$$

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

$$-8x$$