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

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

Evaluate

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

Solution Steps

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

$$11x^{2}-2x^{3}-7+2+x$$

Add -7 and 2 to get -5.

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

Differentiate w.r.t. x

$$1+22x-6x^{2}$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}-2x^{3}-7+2+x)$$

Add -7 and 2 to get -5.

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

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}.

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

Multiply 2 times 11.

$$22x^{2-1}+3\left(-2\right)x^{3-1}+x^{1-1}$$

Subtract 1 from 2.

$$22x^{1}+3\left(-2\right)x^{3-1}+x^{1-1}$$

Multiply 3 times -2.

$$22x^{1}-6x^{3-1}+x^{1-1}$$

Subtract 1 from 3.

$$22x^{1}-6x^{2}+x^{1-1}$$

Subtract 1 from 1.

$$22x^{1}-6x^{2}+x^{0}$$

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

$$22x-6x^{2}+x^{0}$$

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

$$22x-6x^{2}+1$$