Solve (3x^3+4x^2-7x+7)+(9x^3-4x^2-6x)

$$( 3 x ^ { 3 } + 4 x ^ { 2 } - 7 x + 7 ) + ( 9 x ^ { 3 } - 4 x ^ { 2 } - 6 x )$$

Evaluate

$$12x^{3}-13x+7$$

Solution Steps

Combine 3x^{3} and 9x^{3} to get 12x^{3}.

$$12x^{3}+4x^{2}-7x+7-4x^{2}-6x$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x^{3}-7x+7-6x$$

Combine -7x and -6x to get -13x.

$$12x^{3}-13x+7$$

Differentiate w.r.t. x

$$36x^{2}-13$$

Steps Using Derivative Rule for Sum

Combine 3x^{3} and 9x^{3} to get 12x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}+4x^{2}-7x+7-4x^{2}-6x)$$

Combine 4x^{2} and -4x^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-7x+7-6x)$$

Combine -7x and -6x to get -13x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-13x+7)$$

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}.

$$3\times 12x^{3-1}-13x^{1-1}$$

Multiply 3 times 12.

$$36x^{3-1}-13x^{1-1}$$

Subtract 1 from 3.

$$36x^{2}-13x^{1-1}$$

Subtract 1 from 1.

$$36x^{2}-13x^{0}$$

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

$$36x^{2}-13$$