Solve (x^2-11+4x)+(5-9x-3x^2)=

$$( x ^ { 2 } - 11 + 4 x ) + ( 5 - 9 x - 3 x ^ { 2 } ) =$$

Evaluate

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

Solution Steps

Add -11 and 5 to get -6.

$$x^{2}-6+4x-9x-3x^{2}$$

Combine 4x and -9x to get -5x.

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

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

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

Differentiate w.r.t. x

$$-4x-5$$

Steps Using Derivative Rule for Sum

Add -11 and 5 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-6+4x-9x-3x^{2})$$

Combine 4x and -9x to get -5x.

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

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

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

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}.

$$2\left(-2\right)x^{2-1}-5x^{1-1}$$

Multiply 2 times -2.

$$-4x^{2-1}-5x^{1-1}$$

Subtract 1 from 2.

$$-4x^{1}-5x^{1-1}$$

Subtract 1 from 1.

$$-4x^{1}-5x^{0}$$

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

$$-4x-5x^{0}$$

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

$$-4x-5$$