Solve (-5-5x+2x^2)+(-4x^3-4x^2-3)

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

Evaluate

$$-4x^{3}-2x^{2}-5x-8$$

Solution Steps

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-5-5x-2x^{2}-4x^{3}-3$$

Subtract 3 from -5 to get -8.

$$-8-5x-2x^{2}-4x^{3}$$

Differentiate w.r.t. x

$$-12x^{2}-4x-5$$

Steps Using Derivative Rule for Sum

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5-5x-2x^{2}-4x^{3}-3)$$

Subtract 3 from -5 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8-5x-2x^{2}-4x^{3})$$

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}.

$$-5x^{1-1}+2\left(-2\right)x^{2-1}+3\left(-4\right)x^{3-1}$$

Subtract 1 from 1.

$$-5x^{0}+2\left(-2\right)x^{2-1}+3\left(-4\right)x^{3-1}$$

Multiply 2 times -2.

$$-5x^{0}-4x^{2-1}+3\left(-4\right)x^{3-1}$$

Subtract 1 from 2.

$$-5x^{0}-4x^{1}+3\left(-4\right)x^{3-1}$$

Multiply 2 times -2.

$$-5x^{0}-4x^{1}-12x^{3-1}$$

Subtract 1 from 3.

$$-5x^{0}-4x^{1}-12x^{2}$$

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

$$-5x^{0}-4x-12x^{2}$$

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

$$-5-4x-12x^{2}$$