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

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

Evaluate

$$4x^{3}-6x-3$$

Solution Steps

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

$$4x^{3}+2x^{2}-11x-2x^{2}+5x-3$$

Combine 2x^{2} and -2x^{2} to get 0.

$$4x^{3}-11x+5x-3$$

Combine -11x and 5x to get -6x.

$$4x^{3}-6x-3$$

Differentiate w.r.t. x

$$12x^{2}-6$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}+2x^{2}-11x-2x^{2}+5x-3)$$

Combine 2x^{2} and -2x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}-11x+5x-3)$$

Combine -11x and 5x to get -6x.

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

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}.

$$3\times 4x^{3-1}-6x^{1-1}$$

Multiply 3 times 4.

$$12x^{3-1}-6x^{1-1}$$

Subtract 1 from 3.

$$12x^{2}-6x^{1-1}$$

Subtract 1 from 1.

$$12x^{2}-6x^{0}$$

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

$$12x^{2}-6$$