Solve -2x-5x+quad2x^2+4x+3

$$- 2 x - 5 x + \quad 2 x ^ { 2 } + 4 x + 3$$

Evaluate

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

Solution Steps

Combine -2x and -5x to get -7x.

$$-7x+2x^{2}+4x+3$$

Combine -7x and 4x to get -3x.

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

Differentiate w.r.t. x

$$4x-3$$

Steps Using Derivative Rule for Sum

Combine -2x and -5x to get -7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-7x+2x^{2}+4x+3)$$

Combine -7x and 4x to get -3x.

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

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}.

$$-3x^{1-1}+2\times 2x^{2-1}$$

Subtract 1 from 1.

$$-3x^{0}+2\times 2x^{2-1}$$

Multiply 2 times 2.

$$-3x^{0}+4x^{2-1}$$

Subtract 1 from 2.

$$-3x^{0}+4x^{1}$$

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

$$-3x^{0}+4x$$

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

$$-3+4x$$