Solve 2x^2-3x^2+4x-2-3

$$2 x ^ { 2 } - 3 x ^ { 2 } + 4 x - 2 - 3$$

Evaluate

$$-x^{2}+4x-5$$

Solution Steps

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

$$-x^{2}+4x-2-3$$

Subtract 3 from -2 to get -5.

$$-x^{2}+4x-5$$

Differentiate w.r.t. x

$$4-2x$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+4x-2-3)$$

Subtract 3 from -2 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+4x-5)$$

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}.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

$$-2x^{1}+4x^{0}$$

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

$$-2x+4x^{0}$$

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

$$-2x+4\times 1$$

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

$$-2x+4$$