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

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

Evaluate

$$11x^{3}+1$$

Solution Steps

Combine 2x^{3} and 9x^{3} to get 11x^{3}.

$$11x^{3}+7-6$$

Subtract 6 from 7 to get 1.

$$11x^{3}+1$$

Differentiate w.r.t. x

$$33x^{2}$$

Steps Using Derivative Rule for Sum

Combine 2x^{3} and 9x^{3} to get 11x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}+7-6)$$

Subtract 6 from 7 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}+1)$$

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}.

$$3\times 11x^{3-1}$$

Multiply 3 times 11.

$$33x^{3-1}$$

Subtract 1 from 3.

$$33x^{2}$$