Solve (4x^3+2x^2-11x+3)+(7x^3-5x^2-9x)

$$( 4 x ^ { 3 } + 2 x ^ { 2 } - 11 x + 3 ) + ( 7 x ^ { 3 } - 5 x ^ { 2 } - 9 x )$$

Evaluate

$$11x^{3}-3x^{2}-20x+3$$

Solution Steps

Combine 4x^{3} and 7x^{3} to get 11x^{3}.

$$11x^{3}+2x^{2}-11x+3-5x^{2}-9x$$

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$11x^{3}-3x^{2}-11x+3-9x$$

Combine -11x and -9x to get -20x.

$$11x^{3}-3x^{2}-20x+3$$

Differentiate w.r.t. x

$$33x^{2}-6x-20$$

Steps Using Derivative Rule for Sum

Combine 4x^{3} and 7x^{3} to get 11x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}+2x^{2}-11x+3-5x^{2}-9x)$$

Combine 2x^{2} and -5x^{2} to get -3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-3x^{2}-11x+3-9x)$$

Combine -11x and -9x to get -20x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-3x^{2}-20x+3)$$

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}.

$$3\times 11x^{3-1}+2\left(-3\right)x^{2-1}-20x^{1-1}$$

Multiply 3 times 11.

$$33x^{3-1}+2\left(-3\right)x^{2-1}-20x^{1-1}$$

Subtract 1 from 3.

$$33x^{2}+2\left(-3\right)x^{2-1}-20x^{1-1}$$

Multiply 2 times -3.

$$33x^{2}-6x^{2-1}-20x^{1-1}$$

Subtract 1 from 2.

$$33x^{2}-6x^{1}-20x^{1-1}$$

Subtract 1 from 1.

$$33x^{2}-6x^{1}-20x^{0}$$

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

$$33x^{2}-6x-20x^{0}$$

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

$$33x^{2}-6x-20$$