Solve (-3x-2+3x^2)+(-4+5x-6x^2)

$$( - 3 x - 2 + 3 x ^ { 2 } ) + ( - 4 + 5 x - 6 x ^ { 2 } )$$

Evaluate

$$-3x^{2}+2x-6$$

Solution Steps

Subtract 4 from -2 to get -6.

$$-3x-6+3x^{2}+5x-6x^{2}$$

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

$$2x-6+3x^{2}-6x^{2}$$

Combine 3x^{2} and -6x^{2} to get -3x^{2}.

$$2x-6-3x^{2}$$

Differentiate w.r.t. x

$$2-6x$$

Steps Using Derivative Rule for Sum

Subtract 4 from -2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x-6+3x^{2}+5x-6x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-6+3x^{2}-6x^{2})$$

Combine 3x^{2} and -6x^{2} to get -3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x-6-3x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from 1.

$$2x^{0}+2\left(-3\right)x^{2-1}$$

Multiply 2 times -3.

$$2x^{0}-6x^{2-1}$$

Subtract 1 from 2.

$$2x^{0}-6x^{1}$$

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

$$2x^{0}-6x$$

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

$$2\times 1-6x$$

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

$$2-6x$$