Solve 18-3x-6x+x^2+10

$$18-3x-6x+ { x }^{ 2 } +10$$

Evaluate

$$x^{2}-9x+28$$

Solution Steps

Combine -3x and -6x to get -9x.

$$18-9x+x^{2}+10$$

Add 18 and 10 to get 28.

$$28-9x+x^{2}$$

Differentiate w.r.t. x

$$2x-9$$

Steps Using Derivative Rule for Sum

Combine -3x and -6x to get -9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18-9x+x^{2}+10)$$

Add 18 and 10 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(28-9x+x^{2})$$

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}.

$$-9x^{1-1}+2x^{2-1}$$

Subtract 1 from 1.

$$-9x^{0}+2x^{2-1}$$

Subtract 1 from 2.

$$-9x^{0}+2x^{1}$$

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

$$-9x^{0}+2x$$

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

$$-9+2x$$