Solve (-4x+7x-11)+(-x^2-2x)=

$$(-4x+7x-11)+(- { x }^{ 2 } -2x)=$$

Evaluate

$$-x^{2}+x-11$$

Solution Steps

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

$$3x-11-x^{2}-2x$$

Combine 3x and -2x to get x.

$$x-11-x^{2}$$

Differentiate w.r.t. x

$$1-2x$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-11-x^{2}-2x)$$

Combine 3x and -2x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x-11-x^{2})$$

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}.

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

Subtract 1 from 1.

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

Multiply 2 times -1.

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

Subtract 1 from 2.

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

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

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

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

$$1-2x$$